[Question]
  [
*This is one of several challenges left for the community by [Calvin's Hobbies](https://codegolf.stackexchange.com/users/26997/calvins-hobbies).*
Take a "family tree describing" file with lines of the form:
```
[ID] [mother ID] [father ID] [gender] [full name]
```
such as this which describes the first family tree at <http://en.wikipedia.org/wiki/Cousin>:
```
1 ? ? M Adam
2 ? ? F Agatha
3 ? ? M Bill
4 2 1 F Betty
5 2 1 M Charles
6 ? ? F Corinda
7 3 4 M David
8 6 5 F Emma
```
Write a program or function that takes in the file name and two IDs and outputs how those people are blood-related in simplest terms, using the common English names for relations. Input may be via STDIN, ARGV or function arguments but output should be to STDOUT.
## Notes
* IDs are positive integers.
* `?` is used when parentage is not known.
* Assume the graph will be connected and has no cycles.
* You may *not* assume that each person's parents are listed before that person (so a person's parent ID could be greater than their own ID).
* Assume everyone is either male or female and everyone has exactly one mother and exactly one father (of correct gender), although they might be unknown.
* Assume names are unique.
* Names can have spaces in them.
## Blood relations
The following definitions of relationships *R* determine if person *A* is the *R* or person *B*. If two variants of *R* are listed, the first is for female *A* and the second for male *A*. All of these need to be implemented. If multiple definitions match, the earlier one is to be used. Terms in parentheses are gender-neutral terms, which do not need to be implemented but will be reused in further definitions. In definitions involving *N* and *M*, assume *N > 1* and *M > 0*.
* daughter/son: *A* lists *B* as either parent.
* mother/father (parent): *B* lists *A* as either parent.
* sister/brother (sibling): *A* and *B* list the same mother *and* father.
* half-sister/half-brother (sibling): *A* and *B* list the same mother **or** the same father.
* niece/nephew: *A* lists a parent who is the sibling of *B*.
* aunt/uncle: *B* is *A*'s niece or nephew.
* granddaughter/grandson (grandchild): *A* lists a parent who lists *B* as their parent.
* grandmother/grandfather (grandparent): *B* is *A*'s grandchild.
* great-niece/great-nephew: *A* is the grandchild of *C* who is the sibling of *B*.
* great-aunt/great-uncle: *B* is *A*'s great-niece or great-nephew.
* great-granddaughter/son (1st great-grandchild): *A* is a grandchild of *C* who lists *B* as their parent.
* great-grandmother/father (1st great-grandparent): *B* is *A*'s 1st great-grandchild.
* Nth great-granddaughter/son (Nth great-grandchild): *A* is an (N-1)th grandchild of *C* who lists *B* as their parent.
* Nth great-grandmother/father (Nth great-grandparent): *B* is *A*'s Nth great-grandchild.
* Nth great-niece/nephew: *A* is the (N-1)th great-grandchild of *C* who is the sibling of *B*.
* Nth great-aunt/uncle: *B* is *A*'s Nth great-niece of Nth great-nephew.
* cousin: *A* is the grandchild of *C* who is the grandparent of *B*.
* Nth cousin: *A* is the (N-1)th grandchild of *C* who is the (N-1)th grandparent of *B*.
* cousin, M times removed: *A* is the grandchild of *C* who is the Mth grandparent of *B* **or** *A* is the Mth grandchild of *C* who is the grandparent of *B* .
* Nth cousin, M times removed: *A* is the Pth great-grandchild of *C* who is the Qth great-grandparent of *B*, where `N = min(P,Q) + 1` and `M = |P-Q|`.
For `Nth`, write `2nd`, `3rd`, `4th`, `5th` etc.
For `M times`, write `once`, `twice`, `thrice`, `4 times`, `5 times` etc.
## Examples
Assume the following file is used (you don't have to be able to deal with multiple spaces, but I added them for legibility):
```
 1  ?  ? F Agatha
 2  ?  ? M Adam
 3  ?  ? F Betty
 4  1  2 M Bertrand
 5  1  2 F Charlotte
 6  ?  ? M Carl
 7  ?  ? F Daisy
 8  3  4 M David
 9  5  6 F Emma
10  ?  ? M Edward
11  ?  ? F Freya
12  7  8 M Fred
13  9 10 F Grace
14  ?  ? M Gerald
15  ?  ? F Hillary
16 11 12 M Herbert
17 13 14 F Jane
18  ?  ? M James
19 15 16 F Kate
20 17 18 M Larry
21  ? 18 F Mary
```
Then input IDs should map to outputs as follows:
```
 1  2 --> Agatha is not a blood relative to Adam.
 8  3 --> David is the son of Betty.
 9 13 --> Emma is the mother of Grace.
 4  5 --> Bertrand is the brother of Charlotte.
 9  4 --> Emma is the niece of Bertrand.
 5  8 --> Charlotte is the aunt of David.
16  7 --> Herbert is the grandson of Daisy.
 1  9 --> Agatha is the grandmother Emma.
12  5 --> Fred is the great-nephew of Charlotte.
 4 13 --> Bertrand is the great-uncle of Grace.
16  3 --> Herbert is the great-grandson of Betty.
 6 17 --> Carl is the great-grandfather of Jane.
19  2 --> Kate is the 3rd great-granddaughter of Adam.
 1 17 --> Agatha is the 2nd great-grandmother of Jane.
20  4 --> Larry is the 3rd great-nephew of Bertrand.
 5 16 --> Charlotte is the 2nd great-aunt of Herbert.
 8  9 --> David is the cousin of Emma.
19 20 --> Kate is the 4th cousin of Larry.
16  9 --> Herbert is the cousin, twice removed, of Emma.
12 17 --> Fred is the 2nd cousin, once removed, of Jane.
21 20 --> Mary is the half-sister of Larry.
```
I wrote those up by hand so let me know if you spot any mistakes.
*Another set of test data (provided by Scott Leadley, any errors are mine and not Martin's)*
  
Ptolemy family tree
![Ptolemy family tree](https://i.stack.imgur.com/VL8EW.jpg)
  
The picture is illustrative; the data below comes from the Wikipedia article "[Ptolemaic dynasty](http://en.wikipedia.org/wiki/Ptolemaic_dynasty#Ptolemaic_family_tree)".
```
 1  ?  ? F Berenice I of Egypt
 2  ?  ? M Ptolemy I Soter
41  1  2 F Arsinoe II of Egypt
 3  1  2 M Ptolemy II Philadelphus
 4  ?  ? F Arsinoe I of Egypt
 5  ?  ? M Philip
 6  4  3 M Ptolemy III Euergetes
 7  1  5 F Magas of Cyrene
 8  7  ? F Berenice II
 9  8  6 M Ptolemy IV Philopator
10  8  6 F Arsinoe III of Egypt
11 10  9 M Ptolemy V Epiphanes
12  ?  ? F Cleopatra I of Egypt
13 12 11 M Ptolemy VI Philometor
14 12 11 F Cleopatra II
15 12 11 M Ptolemy VIII Physcon
19  ?  ? F Eirene
16 14 13 M Ptolemy VII Neos Philopator
17 14 13 F Cleopatra III
18 14 15 M Ptolemy Memphites
20 19 15 M Ptolemy Apion
21 17 15 F Cleopatra IV
22 17 15 M Ptolemy IX Lathyros
23 17 15 F Cleopatra Selene I
24 17 15 M Ptolemy X Alexander I
25 23 22 F Berenice III of Egypt
26 23 24 M Ptolemy XI Alexander II
27 21 22 M Ptolemy XII Auletes
28 25 24 F Cleopatra V of Egypt
29 28 27 F Cleopatra VI of Egypt
30 28 27 F Berenice IV of Egypt
31 28 27 M Ptolemy XIII Theos Philopator
32 28 27 F Cleopatra VII Thea Philopator
33 28 27 M Ptolemy XIV
34 28 27 F Arsinoe IV of Egypt
35  ?  ? M Julius Caesar
37 32 35 M Ptolemy XV Caesarion
36  ?  ? M Mark Anthony
38 32 36 M Alexander Helios
39 32 36 M Ptolemy XVI Philadelphus
40 32 36 F Cleopatra Selene II
```
  
[Answer]
# Cobra - 932
Out of all the challenges I've answered in Cobra, this is by far one of the best examples of what it can do.
EDIT: It's now a function, but must be prefixed by the signature for Z (included in char count).
```
sig Z(m,n=nil,r=nil)as String?
def f(f='',u='',v='')
    d={:}
    for l in File.readAllLines(f)
        w=l.trim.split
        i,j,k,p=w[:4]
        q=w[4:].join(' ')
        if i==u,x,g=q,if(p<'M',1,0)
        if i==v,y=q
        d.add(i,[j,k])
    o as Z=do(n,m,r)=if(n>1,"[n][if(0<n%10<4and not 10<n%100<14,'stndrd'[n%10-1:n%10+2],'th')] ",'')
    z as Z=do(m,n,r)
        h,a,b=n
        if m[0]==m[1]
            if if(b<1or 0<b<3and a>b,s=2,s=0),a,b=b,a
            r="the [if(a,if(a<2,if(b<2,if(not'?'in'[c=d[u]][e=d[v]]'and c==e,'','half-')+['brother','sister'][g],if(b<3,'',o(b-2)+'great-')+['uncle','aunt','nephew','neice'][s+g]),o(a-1)+'cousin'+if(b>a,', '+if((b-=a)<4,['on','twi','thri'][b-1]+'ce','[b] times')+' removed,','')),if(b,if(b<3,'',o(b-2)+'great-')+'grand','')+['father','mother','son','daughter'][s+g])] of"
        for t in d[m[h]],if'?'<>h,r?=if(h,z([m[0],t],[1,a,b+1]),z(m,[1,a,0])?z([t,v],[0,a+1,0]))
        return r to String?
    print x+" is [z([u,v],[0,0,0])?'not a blood relative to'] [y]."
```
Commented: (out of date, but still the same code-flow)
```
class F
    # Initilaise link dict
    var d={'?':@[''][:0]}
    # Gender bool
    var g
    def main
        # Initilaise name dict
        d={'?':@[''][:0]}
        # Take args
        f,a,b=CobraCore.commandLineArgs[1:]
        # For line in file
        for l in File.readAllLines(f)
            # Split line
            i=l.split
            # Add links to link dict
            .d.add(i[0],i[1:3])
            # Add names to name dict
            d.add(i[0],i[3:])
        # Get gender
        .g=if(d[a][0]=='F',1,0)
        # Print result
        print _
            '[d[a][1]] is '+ _ # Name A
                .r(@[1,0,0],@[a,a,b,b]) _ # If link found, link
                ? _ # Else
                'not a blood relative'+ _ # Not related
            ' of [d[b][1]].' # Name B
    def r(n as int[],m as String[])as String?
        # Recurse through the links at each level from A (A1), climbing when no links are found to B
        # For each level incremented for A, search upwards to the end of all nodes from B (B1), looking for A1
        r=nil
        # Check if we're done searching/climbing
        if m[1]==m[2]
            a,b=n[1:]
            s=if(b<1or b in[1,2]and a>b,1,0)
            if s,a,b=b,a
            # Take the A and B distance and translate them into a phrase
            return'the '+ _ 
                if(a, _
                    if(a<2, _
                        if(b<2, _
                            if('?'not in'[.d[m[0]]][.d[m[3]]]'and.d[m[0]]==.d[m[3]], _
                                '', _
                                'half-' _
                            )+['brother','sister'][.g], _
                            if(b<3, _
                                '', _
                                .o(b-2)+'great-' _
                            )+[['uncle','aunt'],['nephew','neice']][s][.g] _
                        ), _
                        .o(a-1)+'cousin'+if(b>a, _
                            ', '+if((b-=a)<4, _
                                ['once','twice','thrice'][b-1], _
                                '[b] times' _
                            )+' removed,', _
                            '' _
                        ) _
                    ), _
                    if(b, _
                        if(b<3, _
                            '', _
                            '[.o(b-2)]great-' _
                        )+'grand', _
                        '' _
                    )+[['father','mother'],['son','daughter']][s][.g] _
                )
        # Check if we're climbing
        if n[0]
            # For each link in the current A-level
            for x in.d[m[1]]
                r?= _
                    .r(@[0,n[1],0],m) _ # Start a search
                    ? _ # If the search failed
                    .r(@[1,n[1]+1,0],@[m[0],x,m[3],m[3]]) # Climb again
        # Check if we're searching
        else
            # For each link in the current B-level
            for x in.d[m[2]]
                # Search up one level from the current B-level
                r?=.r(@[0,n[1],n[2]+1],@[m[0],m[1],x,m[3]])
        return r
    def o(n as int)as String
        # Get ordinal string for the number
        return if(n>1,'[n][if(0<n%10<4and not 10<n%100<14,['st','nd','rd'][n%10-1],'th')] ','')
```
[Answer]
# ECMAScript 6, 886
Division by zero is a wonderful thing.
This uses quasi-literals once (which are not implemented in Firefox 33 or node.js, but *are* available in the nightly builds of Firefox). The quasi literal used:
```
`
`
```
may be replaced with `"\n"` if whatever you are using lacks support for these.
This script constructs a tree from the list of people, storing both parents and children. Every path from person A to person B is tried, and the optimal path is saved. A path is considered valid if it only changes from going up to going down the tree once. The opposite change is not allowed - if one needs to go down to a children and back up to another parent in order to find a path, the two people are not blood relatives. (`UUUUUDDD` is valid, `UUDUUU` is not. `U` means go up (to a parent), `D` means go down (to a child)).
Sort of golfed:
```
R=(a,b)=>{F="forEach",C='';p=[],g=[],c={},n=[],e=m=1/0;y=i=>i+(k=i%10,k&&k<4&&~~(i%100/10)-1?[,'st ','nd ','rd '][k]:'th ');q=(a,b,s,$)=>!($=$.slice())|!a|~$.indexOf(a)||a-b&&$.push(a)|[p,c][F]((M,N)=>M[a][F](j=>q(j,b,s+N,$)))||(z=(s.match(/0/g)||[]).length,r=s.length-z,_=e+m-z-r,s.indexOf(10)<0&_>0|!_&m>r&&(e=z,m=r));I.split(`
`)[F](V=>{P=V.split(' ');D=+P[0];p[D]=[+P[1],+P[2]];g[D]=P[3]<'L';n[D]=P.slice(4).join(' ');c[D]=[]});p[F]((V,I)=>V[F](Y=>Y&&c[Y].push(I)));q(a,b,C,[]);U=e>m?m:e,V=e>m?e:m;alert(n[a]+' is '+(e/m+1?'the '+(U*V---1?U<2?(V<3?C:y(V-1))+(V<2?C:'great-')+(V*!U?'grand':C)+'son0father0nephew0uncle0daughter0mother0niece0aunt'.split(0)[g[a]*4+2*U+(U==e)]:(V-=--U,(U<2?C:y(U))+'cousin'+(V?', '+(V>3?V+' times':[,'on','twi','thri'][V]+'ce')+' removed,':C)):(p[a].join()==p[b].join()?C:'half-')+(g[a]?'sister':'brother'))+' of ':'not a blood relative to ')+n[b]+'.')}
```
Ungolfed (kind of):
```
// function for running.
R=(a,b)=>{
F="forEach",C='';
p=[], g=[], c={}, n=[], e=m=1/0;
// returns suffixed number (1->1st, 2->2nd, etc)
y= i=>i+(k=i%10,k&&k<4&&~~(i%100/10)-1?[,'st ','nd ','rd '][k]:'th ');
// this looks for the shortest path up/down the family tree between a and b.
q=(a,b,s,$)=>
  // copy the array of visited people
  !($=$.slice())
  // check if a is invalid
  | !a
  // check to make sure we are not visiting a for a second time
  | ~$.indexOf(a)
  // if a != b
  || a-b 
  // add a to visited, and call q(...) on all parents and children
  && $.push(a) |
   [p,c][F]((M,N)=>M[a][F](j=>q(j,b,s+N,$)))
  || (
    // a == b
    // get number of ups and downs
    z=(s.match(/0/g)||[]).length,
    r=s.length-z,
    _=e+m-z-r,
    // if DU: path is invalid.
    // if _>0: path is shorter
    // if _==0: check m > r to see if new path should replace old 
    s.indexOf(10)<0 & _>0|!_&m>r && (e=z,m=r));
// load list of people into arrays
I.split(`
`)[F](V=>{
  P=V.split(' ');
  // ID
  D=+P[0];
  // parents: NaN if not given
  p[D]=[+P[1],+P[2]];
  // gender: 1 if female, 0 if male
  g[D]=P[3]<'L';
  // merge the rest of the array to get name
  n[D]=P.slice(4).join(' ');
  // empty children array..for now
  c[D]=[]
});
// push current ID to parents' children array.
p[F]((V,I)=>V[F](Y=>Y&&c[Y].push(I)));
// get shortest path
q(a,b,C,[]);
U=e>m?m:e,V=e>m?e:m;
G=(a,b,c,d)=>(a<3?C:y(a-1))+(a<2?C:'great-')+(a*!b?'grand':C)+'son0father0nephew0uncle0daughter0mother0niece0aunt'.split(0)[g[d]*4+2*b+(b==c)];
// output
alert(n[a]+' is '+(e/m+1?'the '+(U*V---1?
    U<2?
        G(V,U,e,a)
    :(V-=--U,
     (U<2?C:y(U))+'cousin'+
     (V?
        ', '+(V>3?V+' times':[,'on','twi','thri'][V]+'ce')+' removed,'
     :C)
     )
:(p[a].join()==p[b].join()?C:'half-')+(g[a]?'sister':'brother'))+' of ':'not a blood relative to ')+n[b]+'.')
}
```
Notes:
* List of people should be placed in a variable `I` (as a string, with single spaces and newlines).
* To call: `R(a,b)`, where `a` and `b` are the IDs of the two people being compared.
[Answer]
## C - ungolfed
```
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
typedef enum {
    MALE,
    FEMALE
} gender_t;
typedef enum {
    VISITED_A,
    VISITED_B,
    NOT_VISITED
} visited_t;
struct node {
    int id;
    int mother;
    int father;
    char *name;
    int height;
    gender_t gender;
    visited_t visited;
};
struct queue_item {
    void *item;
    struct queue_item *next;
    struct queue_item *previous;
};
struct queue {
    struct queue_item *first;
    struct queue_item *last;
};
void queue_push(struct queue *q, struct node *n)
{
    struct queue_item *i = malloc(sizeof(*i));
    i->item = (void *)n;
    i->next = q->last;
    i->previous = NULL;
    q->last = i;
    if(i->next != NULL) {
        i->next->previous = i;
    } else {
        q->first = i;
    }
}
void queue_pop(struct queue *q)
{
    struct queue_item *temp = q->first;
    if(temp) {
        q->first = q->first->previous;
        if(q->first == NULL) {
            q->last = NULL;
        } else {
            q->first->next = NULL;
        }
        free(temp);
    }
}
struct node *queue_front(struct queue *q)
{
    if(q->first) {
        return (struct node *)q->first->item;
    } else {
        return NULL;
    }
}
void queue_free(struct queue *q) {
    while(queue_front(q) != NULL) {
        queue_pop(q);
    }
    free(q);
}
struct node *find_shortest_path(struct node **nodes, struct node *a, struct node *b)
{
    struct queue *q = malloc(sizeof(*q));
    q->first = NULL;
    q->last = NULL;
    a->visited = VISITED_A;
    queue_push(q, a);
    b->visited = VISITED_B;
    queue_push(q, b);
    struct node *n, *father, *mother;
    while((n = queue_front(q)) != NULL) {
        if(n->visited == VISITED_A) {
            if(n->father != 0) {
                father = nodes[n->father-1];
                if(father->visited == VISITED_B) {
                    a->height = n->height + 1;
                    b->height = father->height;
                    n = father;
                    goto exit_queue_free;
                } else  if(father->visited == NOT_VISITED) {
                    father->visited = VISITED_A;
                    father->height = n->height+1;
                    queue_push(q, father);
                }
            }
            if(n->mother != 0) {
                mother = nodes[n->mother-1];
                if(mother->visited == VISITED_B) {
                    a->height = n->height + 1;
                    b->height = mother->height;
                    n = mother;
                    goto exit_queue_free;
                } else  if(mother->visited == NOT_VISITED) {
                    mother->visited = VISITED_A;
                    mother->height = n->height+1;
                    queue_push(q, mother);
                }
            }
        } else if (n->visited == VISITED_B) {
            if(n->father != 0) {
                father = nodes[n->father-1];
                if(father->visited == VISITED_A) {
                    b->height = n->height + 1;
                    a->height = father->height;
                    n = father;
                    goto exit_queue_free;
                } else  if(father->visited == NOT_VISITED) {
                    father->visited = VISITED_B;
                    father->height = n->height+1;
                    queue_push(q, father);
                }
            }
            if(n->mother != 0) {
                mother = nodes[n->mother-1];
                if(mother->visited == VISITED_A) {
                    b->height = n->height + 1;
                    a->height = mother->height;
                    n = mother;
                    goto exit_queue_free;
                } else  if(mother->visited == NOT_VISITED) {
                    mother->visited = VISITED_B;
                    mother->height = n->height+1;
                    queue_push(q, mother);
                }
            }
        }
        queue_pop(q);
    }
exit_queue_free:
    queue_free(q);
    return n;
}
int main(int argc, char *argv[]) {
    if(argc != 4) {
        return -1;
    }
    FILE *file = fopen(argv[1], "r");
    int id_1 = strtol(argv[2], NULL, 0);
    int id_2 = strtol(argv[3], NULL, 0);
    char name[128];
    char id[128];
    char id_father[128];
    char id_mother[128];
    char gender;
    struct queue *read_queue = malloc(sizeof(*read_queue));
    read_queue->first = NULL;
    read_queue->last = NULL;
    int nr_nodes = 0;
    while(fscanf(file, "%s %s %s %c %s",
        id, id_mother, id_father, &gender, name) == 5) {
        struct node *n = malloc(sizeof(*n));
        if(strcmp(id, "?") == 0) {
            n->id = 0;
        } else {
            n->id = strtol(id, NULL, 0);
        }
        if(strcmp(id_mother, "?") == 0) {
            n->mother = 0;
        } else {
            n->mother = strtol(id_mother, NULL, 0);
        }
        if(strcmp(id_father, "?") == 0) {
            n->father = 0;
        } else {
            n->father = strtol(id_father, NULL, 0);
        }
        if(gender == 'M') {
            n->gender = MALE;
        } else {
            n->gender = FEMALE;
        }
        n->name = malloc(strlen(name)+1);
        strcpy(n->name, name);
        n->visited = NOT_VISITED;
        n->height = 0;
        queue_push(read_queue, n);
        nr_nodes++;
    }
    struct node **nodes = malloc(sizeof(*nodes) * nr_nodes);
    struct node *temp;
    while((temp = queue_front(read_queue)) != NULL) {
        nodes[temp->id-1] = temp;
        queue_pop(read_queue);
    }
    queue_free(read_queue);
    struct node *a = nodes[id_1-1], *b = nodes[id_2-1];
    temp = find_shortest_path(nodes, a, b);
    if(temp) {
        if(a->height == b->height) {
            if(a->height == 1) {
                if((a->father == b->father) &&
                    (a->mother == b->mother)) {
                    printf("%s is the %s of %s.\n", a->name,
                        a->gender == MALE ?
                        "brother" : "sister",
                        b->name);
                } else {
                    printf("%s is the half-%s of %s.\n",
                        a->name,
                        a->gender == MALE ?
                        "brother" : "sister",
                        b->name);
                }
            } else if (a->height == 2) {
                printf("%s is the cousin of %s.\n", a->name,
                    b->name);
            } else if (a->height == 3){
                printf("%s is the 2nd cousin of %s.\n", a->name,
                    b->name);
            } else if (a->height == 4) {
                printf("%s is the 3rd cousin of %s.\n", a->name,
                    b->name);
            } else {
                printf("%s is the %dth cousin of %s.\n", a->name,
                    a->height-1,b->name);
            }
        } else if (a->height == 0) {
            if(b->height == 1) {
                printf("%s is the %s of %s.\n", a->name,
                    a->gender == MALE ? "father" :
                    "mother", b->name);
            } else if (b->height == 2) {
                printf("%s is the grand%s of %s.\n", a->name,
                    a->gender == MALE ? "father" :
                    "mother", b->name);
            } else if (b->height == 3) {
                printf("%s is the great-grand%s of %s.\n",
                    a->name, a->gender == MALE ?
                    "father" : "mother", b->name);
            } else if (b->height == 4) {
                printf("%s is the 2nd great-grand%s of %s.\n",
                    a->name, a->gender == MALE ?
                    "father" : "mother", b->name);
            } else if (b->height == 5) {
                printf("%s is the 3rd great-grand%s of %s.\n",
                    a->name, a->gender == MALE ?
                    "father" : "mother", b->name);
            } else if (b->height == 6) {
                printf("%s is the %dth great-grand%s of %s.\n",
                    a->name, b->height-2,
                    a->gender == MALE ? "father" :
                    "mother", b->name);
            }
        } else if (b->height == 0) {
            if(a->height == 1) {
                printf("%s is the %s of %s.\n", a->name,
                    a->gender == MALE ? "son" :
                    "daughter", b->name);
            } else if (a->height == 2) {
                printf("%s is the grand%s of %s.\n", a->name,
                    a->gender == MALE ? "son" :
                    "daughter", b->name);
            } else if (a->height == 3) {
                printf("%s is the great-grand%s of %s.\n",
                    a->name, a->gender == MALE ?
                    "son" : "daughter", b->name);
            } else if (a->height == 4) {
                printf("%s is the 2nd great-grand%s of %s.\n",
                    a->name, a->gender == MALE ?
                    "son" : "daughter", b->name);
            } else if (a->height == 5) {
                printf("%s is the 3rd great-grand%s of %s.\n",
                    a->name, a->gender == MALE ?
                    "son" : "daughter", b->name);
            } else {
                printf("%s is the %dth great-grand%s of %s.\n",
                    a->name, a->height - 2,
                    a->gender == MALE ? "son" :
                    "daughter", b->name);
            }
        } else if (a->height == 1) {
            if(b->height == 2) {
                printf("%s is the %s of %s.\n", a->name,
                    a->gender == MALE ? "uncle" :
                    "aunt", b->name);
            } else if(b->height == 3) {
                printf("%s is the great-%s of %s.\n", a->name,
                    a->gender == MALE ? "uncle" :
                    "aunt", b->name);
            } else if(b->height == 4) {
                printf("%s is the 2nd great-%s of %s.\n", a->name,
                    a->gender == MALE ? "uncle" :
                    "aunt", b->name);
            } else if(b->height == 5) {
                printf("%s is the 3rd great-%s of %s.\n", a->name,
                    a->gender == MALE ? "uncle" :
                    "aunt", b->name);
            } else {
                printf("%s is the %dth great-%s of %s.\n",
                    a->name, b->height - 2,
                    a->gender == MALE ? "uncle" :
                    "aunt", b->name);
            }
        } else if (b->height == 1) {
            if(a->height == 2) {
                printf("%s is the %s of %s.\n", a->name,
                    a->gender == MALE ? "nephew" :
                    "niece", b->name);
            } else if(a->height == 3) {
                printf("%s is the great-%s of %s.\n", a->name,
                    a->gender == MALE ? "nephew" :
                    "niece", b->name);
            } else if(a->height == 4) {
                printf("%s is the 2nd great-%s of %s.\n", a->name,
                    a->gender == MALE ? "nephew" :
                    "niece", b->name);
            } else if(a->height == 5) {
                printf("%s is the 3rd great-%s of %s.\n", a->name,
                    a->gender == MALE ? "nephew" :
                    "niece", b->name);
            } else {
                printf("%s is the %dth great-%s of %s.\n",
                    a->name, a->height - 2,
                    a->gender == MALE ? "nephew" :
                    "niece", b->name);
            }
        } else {
            int m = a->height > b->height ? a->height - b->height :
                b->height - a->height;
            int n = a->height > b->height ? b->height - 1:
                a->height - 1;
            printf("%s is the ", a->name);
            if(n == 2) printf("2nd ");
            if(n == 3) printf("3rd ");
            if(n > 3) printf("%dth ", n);
            printf(" cousin, ");
            if (m == 1) printf("once");
            if (m == 2) printf("twice");
            if (m == 3) printf("thrice");
            if (m > 3) printf("%d times", m);
            printf(" removed, of %s.\n", b->name);
        }
    } else
        printf("%s is not a blood relative to %s.\n", a->name, b->name);
    int i;
    for(i = 0; i < nr_nodes; i++) {
        free(nodes[i]->name);
        free(nodes[i]);
    }
    free(nodes);
    fclose(file);
    return 0;
}
```
[Answer]
### Ruby - ~~1892~~ ~~1290~~ 1247
Run as `ruby relation.rb ID1 ID2 relationship_file`.
```
P=Struct.new(:i,:m,:f,:s,:n,:c)
def f u,v,w,x,y,z
t=[y,z,v]
return t if v=='?'||x.include?(v)||v==w
r=x+[v];p=u[v]
p.c.each{|o|s=f(u,o,w,r,y,z+1);return s if s.last==w}
return t if z>0
[:m,:f].each{|i|s=f(u,p[i],w,r,y+1,z);return s if s.last==w}
t;end
def g j,a,r,b;puts"#{j[a].n} is the #{r} of #{j[b].n}.";end
def k n;n<2?'':n<3?'2nd':n<4?'3rd':"#{n}th";end
def h n;n<2?'':n<3?'great-':"#{k(n-1)} great-";end
def e n;s=n<2?'once':n<3?'twice':n<4?'thrice':"#{n} times";", #{s} removed,";end
def d u,a,b,x;y,z=x
if y==1&&z==1
w=u[a];v=u[b]
g(u,a,((w.f==v.f&&w.m==v.m)?'':'half-')+((w.s=='F')?'sister':'brother'),b)
elsif y<1||z<1
t=[y,z].max
g(u,a,h(t-1)+(t>=2?'grand':'')+(u[a].s=='F'?y>0?'daughter':'mother':y>0?'son':'father'),b)
elsif y==1||z==1
t=[y,z].max
g(u,a,h(t-1)+(u[a].s=='F'?y==1?'aunt':'niece':y==1?'uncle':'nephew'),b)
else
s=[y,z].min
g(u,a,(s-1>1?"#{k(s-1)} ":'')+'cousin'+((y==z)?'':e((z-y).abs)),b)
end;end
A,B=$*.shift(2);j={}
ARGF.each_line{|l|a=l.scan(/\s*(\d+)\s+(\d+|\?)\s+(\d+|\?)\s+([MF])\s+([\w\s]*\w+)\s*/).flatten;j[a[0]]=P.new(a[0],a[1],a[2],a[3],a[4],[])}
j.each{|k,i|[:f,:m].each{|l|j[i[l]].c<<k if i[l]!='?'}}
a=f(j,A,B,[],0,0)
if a.pop==B
d(j,A,B,a)
else
puts"#{j[A].n} is not a blood relative to #{j[B].n}."
```
Ungolfed version - ~~5251~~ 3416 (same call tree, just did a lot of code folding)
```
Person = Struct.new( :id, :mother, :father, :sex, :name, :children )
#       Find a path between "start" and "finish". To reflect human consanguinity
# rules, either travel down through descendants or up through ancestors with a
# possible down leg through their descendants.
#
# Use depth-first search until forced to improve.
# If start up, path allowed one inflection point.
# Once start down, path must continue down.
# returns [stepsUp, stepsDown, trialResult],
#   shortest path found if trialResult == finish
def findRelationship(people, start, finish, pathSoFar, stepsUp, stepsDown)
  trialResult = [stepsUp, stepsDown, start]
  #     Return success or failure.
  return trialResult if start == '?' || pathSoFar.include?(start) || start == finish
  #     If success or failure not known, explore further.
  pathNext = pathSoFar + [start]
  person = people[start]
  #     Follow descendants.
  person[:children].each do |child|
    trial = findRelationship(people, child, finish, pathNext, stepsUp, stepsDown+1)
    return trial  if trial.last == finish
  end
  #     Already past inflection point?
  return trialResult  if stepsDown > 0
  #     Follow ancestry.
  [:mother, :father].each do |parent|
    trial = findRelationship(people, person[parent], finish, pathNext, stepsUp+1, stepsDown)
    return trial  if trial.last == finish
  end
  return trialResult
end
def printRelationship(people, a, relationship, b)
  puts "#{people[a][:name]} is the #{relationship} of #{people[b][:name]}."
end
def formatNth(n)
  return n<2?'':n<3?'2nd':n<4?'3rd':"#{n}th"
end
def formatGenerations(n)
  return n<2?'':n<3?'great-':"#{formatNth(n-1)} great-"
end
def formatRemoves(n)
  s=n<2?'once':n<3?'twice':n<4?'thrice':"#{n} times"
  return ", #{s} removed,"
end
def describeRelationship(people, a, b, legLengths)
  down = legLengths.pop
  up = legLengths.pop
  if up==1 && down==1
    who = people[a]
    what = people[b]
    printRelationship(people, a,
        (who[:father] == what[:father]  &&  who[:mother] == what[:mother] ? '' : 'half-') +
          ((who[:sex] == 'F') ? 'sister' : 'brother'),
        b)
  elsif up<1 || down<1
    pathLength = [up, down].max
    printRelationship(people, a,
        formatGenerations(pathLength-1) + ((pathLength>=2) ? 'grand' : '') +
          (up>0 ?
            people[a][:sex] == 'F' ? 'daughter' : 'son'  :
            people[a][:sex] == 'F' ? 'mother': 'father'
          ),
        b)
  elsif up==1 || down==1
    pathLength = [up, down].max
    printRelationship(people, a,
        formatGenerations(pathLength-1) +
          (up==1 ?
            people[a][:sex] == 'F' ? 'aunt': 'uncle'  :
            people[a][:sex] == 'F' ? 'niece': 'nephew'
          ),
        b)
  else
    shortestLeg = [up, down].min
    printRelationship(people, a,
        (shortestLeg-1>1 ? "#{formatNth(shortestLeg-1)} " : '') +
          'cousin' +
          (up==down ? '' : formatRemoves((down-up).abs)),
        b)
  end
end
A = $*.shift
B = $*.shift
#       Meet and greet.
people = {}
ARGF.each_line do |line|
  a = line.scan(/\s*(\d+)\s+(\d+|\?)\s+(\d+|\?)\s+([MF])\s+([\w\s]*\w+)\s*/).flatten
  people[a[0]] = Person.new( a[0], a[1], a[2], a[3], a[4], [] )
end
#       Build lineage.
people.each do |key, individual|
  [:father, :mother].each do |l|
      people[individual[l]][:children] << key  if individual[l] != '?'
  end
end
#       How are A and B related?
a = findRelationship(people, A, B, [], 0, 0)
if a.pop == B
  describeRelationship(people, A, B, a)
else
  puts "#{people[A][:name]} is not a blood relative to #{people[B][:name]}."
end
```
Passes the following test suite:
```
#!/usr/bin/env perl
#
use strict;
use warnings;
require File::Temp;
use File::Temp qw( tempfile tempdir );
use Test::More qw(no_plan);
# use Test::More tests => 38;
#       solution executable
my $solver='ruby relation.rb';
#       "happy" path
my $dir = tempdir( CLEANUP => 1 );
my ($fh, $filename) = tempfile( DIR => $dir );
my $testData = <<'END_TEST_DATA';
 1  ?  ? F Agatha
 2  ?  ? M Adam
 3  ?  ? F Betty
 4  1  2 M Bertrand
 5  1  2 F Charlotte
 6  ?  ? M Carl
 7  ?  ? F Daisy
 8  3  4 M David
 9  5  6 F Emma
10  ?  ? M Edward
11  ?  ? F Freya
12  7  8 M Fred
13  9 10 F Grace
14  ?  ? M Gerald
15  ?  ? F Hillary
16 11 12 M Herbert
17 13 14 F Jane
18  ?  ? M James
19 15 16 F Kate
20 17 18 M Larry
21  ? 18 F Mary
END_TEST_DATA
print $fh  $testData;
close($fh);
is( `$solver 1  2 $filename 2>&1`, "Agatha is not a blood relative to Adam.\n", 'OP example #1,  1  2');
is( `$solver 8 3 $filename 2>&1`, "David is the son of Betty.\n", 'OP example #2,  8  3');
is( `$solver 9 13 $filename 2>&1`, "Emma is the mother of Grace.\n", 'OP example #3,  9 13');
is( `$solver 4 5 $filename 2>&1`, "Bertrand is the brother of Charlotte.\n", 'OP example #4,  4  5');
is( `$solver 9 4 $filename 2>&1`, "Emma is the niece of Bertrand.\n", 'OP example #5,  9  5');
is( `$solver 5 8 $filename 2>&1`, "Charlotte is the aunt of David.\n", 'OP example #6,  5  8');
is( `$solver 16 7 $filename 2>&1`, "Herbert is the grandson of Daisy.\n", 'OP example #7, 16  7');
is( `$solver 1 9 $filename 2>&1`, "Agatha is the grandmother of Emma.\n", 'OP example #8,  1  9 (amended)');
is( `$solver 12 5 $filename 2>&1`, "Fred is the great-nephew of Charlotte.\n", 'OP example #9, 12  5');
is( `$solver 4 13 $filename 2>&1`, "Bertrand is the great-uncle of Grace.\n", 'OP example #10,  4 13');
is( `$solver 16 3 $filename 2>&1`, "Herbert is the great-grandson of Betty.\n", 'OP example #11, 16  3');
is( `$solver 6 17 $filename 2>&1`, "Carl is the great-grandfather of Jane.\n", 'OP example #12,  6 17');
is( `$solver 19 2 $filename 2>&1`, "Kate is the 3rd great-granddaughter of Adam.\n", 'OP example #13, 19  2 (amended)');
is( `$solver 1 17 $filename 2>&1`, "Agatha is the 2nd great-grandmother of Jane.\n", 'OP example #14,  1 17 (amended)');
is( `$solver 20 4 $filename 2>&1`, "Larry is the 3rd great-nephew of Bertrand.\n", 'OP example #15, 20  4');
is( `$solver 5 16 $filename 2>&1`, "Charlotte is the 2nd great-aunt of Herbert.\n", 'OP example #16,  5 16');
is( `$solver 8 9 $filename 2>&1`, "David is the cousin of Emma.\n", 'OP example #17,  8  9');
is( `$solver 19 20 $filename 2>&1`, "Kate is the 4th cousin of Larry.\n", 'OP example #18, 19 20');
is( `$solver 16 9 $filename 2>&1`, "Herbert is the cousin, twice removed, of Emma.\n", 'OP example #19, 16  9');
is( `$solver 12 17 $filename 2>&1`, "Fred is the 2nd cousin, once removed, of Jane.\n", 'OP example #20, 12 17');
is( `$solver 21 20 $filename 2>&1`, "Mary is the half-sister of Larry.\n", 'OP example #21, 21 20');
#       "sad" path
# none!
#       "bad" path
# none!
exit 0;
```
[Answer]
# Javascript, 2292
```
for(var r=prompt().split("\n"),n=[{m:"",f:""}],t=1;t<r.length;t++){var e=r[t].split(" ");n[+e[0]]={m:"?"==e[1]?-1:+e[1],f:"?"==e[2]?-1:+e[2],s:e[3],n:e[4]}}var f=function(r,t){return r=n[r],t=n[t],~r.m&&r.m==t.m&&~r.f&&r.f==t.f?"M"==r.s?"brother":"sister":void 0},i=function(r,t){return r=n[r],t=n[t],~r.m&&r.m==t.m||~r.f&&r.f==t.f?"M"==r.s?"half-brother":"half-sister":void 0},o=function(r){var n=("0"+r).slice(-2),t=n[0];return n=n[1],r+(1==t?"th":1==n?"st":2==n?"nd":3==n?"rd":"th")+" "},a=function(r){return 1==r?"once":2==r?"twice":3==r?"thrice":r+" times"},h=function(r,t){var e,f,i=[t],a=[n[t].m,n[t].f];for(e=0;e<n.length&&!~a.indexOf(r);e++){i=a.slice(),a=[];for(var h=0;h<i.length;h++)i[h]>=0&&a.push(n[i[h]].m,n[i[h]].f)}if(!(e>=n.length))return f="M"==n[r].s?"father":"mother",e>0&&(f="grand"+f),e>1&&(f="great-"+f),e>2&&(f=o(e-1)+f),f},u=function(r,t){var e=h(t,r);return e?e.slice(0,-6)+("M"==n[r].s?"son":"daughter"):void 0},s=function(r){for(var t=[],e=1;e<n.length;e++)f(r,e)&&e!=r&&t.push(e);return t},l=function(r){return r=r.slice(0,-6),""==r?r:"grand"==r?"great ":"great-grand"==r?"2nd great ":o(+r.split(" ")[0].slice(0,-2)+1)+"great "},v=function(r,t){for(var e,f=s(r),i=0;i<f.length&&!(e=h(f[i],t));i++);return e?l(e)+("M"==n[r].s?"uncle":"aunt"):void 0},c=function(r,t){var e=v(t,r);return e?(e.split(" ").slice(0,-1).join(" ")+("M"==n[r].s?" nephew":" niece")).trim():void 0},g=function(r,n){for(var t=0;t<r.length;t++)if(~n.indexOf(r[t]))return!0},m=function(r,t){r=n[r],t=n[t];for(var e=[[r.m,r.f]],f=[[t.m,t.f]],i=0;i<n.length;i++){for(var h=e[i],u=f[i],s=[],l=0;l<h.length;l++){var v=0,c=0;-1!=h[l]&&(v=n[h[l]].m,c=n[h[l]].f),v>0&&s.push(v),c>0&&s.push(c)}for(var m=[],l=0;l<u.length;l++){var v=0,c=0;-1!=u[l]&&(v=n[u[l]].m,c=n[u[l]].f),v>0&&m.push(v),c>0&&m.push(c)}if(!s.length&&!m.length)break;e.push(s),f.push(m)}for(var i=1;i<Math.min(e.length,f.length);i++){var h=e[i],u=f[i];if(g(h,u))return(i>1?o(i):"")+"cousin"}for(var i=1;i<e.length;i++)for(var h=e[i],l=1;l<f.length;l++){var u=f[l];if(g(h,u)){var p=Math.min(i,l);return(p>1?o(p):"")+"cousin, "+a(Math.abs(i-l))+" removed,"}}},e=prompt().split(" "),p=+e[0],d=+e[1],M=u(p,d)||h(p,d)||f(p,d)||i(p,d)||c(p,d)||v(p,d)||m(p,d);alert(n[p].n+" is "+(M?"the "+M+" of ":"not a blood relative to ")+n[d].n+".\n"
```
I'm sure it can be golfed much further, all I did was put an ungolfed version through a minifier.
You can [run the ungolfed version here on jsFiddle](http://jsfiddle.net/peterolson/pmbbws1k/15/). Here is the output for the example data:
```
1 2 Agatha is not a blood relative to Adam.
8 3 David is the son of Betty.
9 13 Emma is the mother of Grace.
4 5 Bertrand is the brother of Charlotte.
9 4 Emma is the niece of Bertrand.
5 8 Charlotte is the aunt of David.
16 7 Herbert is the grandson of Daisy.
1 9 Agatha is the grandmother of Emma.
12 5 Fred is the great nephew of Charlotte.
4 13 Bertrand is the great uncle of Grace.
16 3 Herbert is the great-grandson of Betty.
6 17 Carl is the great-grandfather of Jane.
19 1 Kate is the 3rd great-granddaughter of Agatha.
2 17 Adam is the 2nd great-grandfather of Jane.
20 4 Larry is the 3rd great nephew of Bertrand.
5 16 Charlotte is the 2nd great aunt of Herbert.
8 9 David is the cousin of Emma.
19 20 Kate is the 4th cousin of Larry.
16 9 Herbert is the cousin, twice removed, of Emma.
12 17 Fred is the 2nd cousin, once removed, of Jane.
21 20 Mary is the half-sister of Larry.
```
[Answer]
# Python 3: 1183
```
def D(i):
 if i==a:return 0
 r=[D(c)for c in t[i][4]]
 if r:return min(x for x in r if x is not None)+1
def A(i):
 if i=="?":return None
 r=D(i)
 if r is not None:return 0,r
 m,f=map(A,t[i][:2])
 return(f[0]+1,f[1])if not m or(f and sum(f)<sum(m))else(m[0]+1,m[1])if f else None
def P(r):print("%s is %s of %s"%(t[a][3],r,t[b][3]))
O=lambda n:"%d%s "%(n,{2:"nd",3:"rd"}.get(n,"th"))
G=lambda n:(O(n-2)if n>3 else"")+("great-"if n>2 else"")
GG=lambda n:G(n)+("grand"if n>1 else"")
f,a,b=input().split()
t={}
for l in open(f):
 i,m,f,g,n=l.strip().split(maxsplit=4)
 t[i]=(m,f,g,n,[])
for i,(m,f,g,n,c)in t.items():
 if m in t:t[m][4].append(i)
 if f in t:t[f][4].append(i)
g=t[a][2]=="M"
r=A(b)
if r:
 u,d=r
 if u==d==1:P("the "+("half-"if t[s][0]!=t[e][0]or t[s][1]!=t[s][1]else"")+["sister","brother"][g])
 elif u==0:P("the "+GG(d)+["daughter","son"][g])
 elif d==0:P("the "+GG(u)+["mother","father"][g])
 elif u==1:P("the "+G(d)+["niece","nephew"][g])
 elif d==1:P("the "+G(u)+["aunt","uncle"][g])
 else:
  n,m=min(u,d)-1,abs(u-d);P("the "+(O(n)if n>1 else"")+"cousin"+(" %s removed"%{1:"once",2:"twice",3:"thrice"}.get(m,"%d times"%m)if m else""))
else:
 P("not a blood relative")
```
The filename and the IDs of the people to be described are are read from standard input on a single line.
The top part of the code is function definitions. The script starts half-way down, and first works on processing the input (parsing the file, then assigning children to their parents in a second pass).
After the data is set up, we call the `A` function once to kick off a recursive search. The result defines the relationship.
The rest of the code is dedicated to describing that relationship in English. Siblings and cousins are complicated (and use long lines), the rest are pretty straight forward.
Example run (the second line is my input):
```
C:\>Python34\python.exe relations.py
relations.txt 20 4
Larry is the 3rd great-nephew of Bertrand
```
Function and variable name key:
* `f`: The filename the family's data is read from.
* `a`: The id of the person who's relationship we're naming.
* `b`: The id of the person the relationship is defined relative to.
* `t`: The family tree itself, as a dictionary mapping from an id to a 5-tuple of mother's id, father's id, sex, name and a list of children.
* `g`: A Boolean value reflecting the gender of person `a`. It is `True` if they are a male.
* `u`: The number of generations from `b` to the common ancestor of `a` and `b` (or 0 if `b` is `a`'s ancestor).
* `d`: The number of generations from `a` to the common ancestor of `a` and `b` (or 0 if `a` is `b`'s ancestor).
* `D(i)`: Recursively search the descendents of person `i` for person `a`. Return the depth `a` was found at, or None if it was not found.
* `A(i)`: Recursively search `i` and `i`'s descendents, but if its not found recursively search `i`'s ancestors (and their descendents) too. Returns a 2-tuple, who's values are `u` and `d` described above. If a relationship is found through both parents, the one with the smallest number of generational steps (`u+d`) is preferred. If person `a` has no blood relationship to person `i`, `A(i)` returns `None`.
* `P(r)`: Print result string `r` bracketed by the names of persons `a` and `b`.
* `O(n)`: Return an ordinal string for the given number `n`. Only supports `1 < n < 21`.
* `G(n)`: Return a prefix string equivalent to `n-1` "greats" (e.g. `"2nd great-"` for n=2`). Will return an empty string for n <= 1.
* `GG(n)`: Returns a prefix string with "Nth great-" and "grand", as appropriate for `n` generations. Will return an empty string for n <= 1.
I took a few shortcuts in the name of shorter code which could be revised for better (or slightly more correct) performance on large genealogies. The `A` function doesn't make any attempt to avoid recursing down child trees that have already been searched, which makes it slower than necessary (though probably still fast enough for reasonable sized families). The `O` function doesn't correctly handle ordinals greater than 20 (it's a bit tricky to get all of `11th`, `21st`, and `101st` right, but in one of my draft versions I did it in about 25 additional bytes). Unless you're dealing with very old and famous families (e.g. some of the royal families of Europe) I'm not sure I'd trust the accuracy of a genealogy that went back that far anyway.
On the other hand, I've also skipped over a few places where I could shave off a few bytes. For instance, I could save 3 bytes by renaming `GG` to a single character name, but basing the name off of `great-grand` seemed more worth while to me.
I believe that all white-space in the code is required, but it's possible that some can be skipped and I've just missed them (I kept finding stray spaces in argument lists as I was typing up this answer, but I think I've gotten them all now).
Because my recursive matching requires a relatively simple rule for which relationships to prefer if there is more than one, I don't give exactly the requested results in some obscure cases involving intergenerational incest. For instance, if person `a` is both person `b`'s uncle and grandfather, my code will prefer the grandfather relationship despite the question saying that the uncle relationship should have higher precedence.
Here's an example dataset that exposes the issue:
```
1 ? ? F Alice
2 1 ? M Bob
3 1 2 F Claire
4 3 ? F Danielle
```
I suspect that for most programs, the relationships between Bob and Claire or between Bob and Danielle will cause trouble. They will either call the first pair half-siblings rather than father/daughter or they'll describe the latter pair as grandfather/granddaughter rather than uncle/niece. My code does the latter, and I don't see any reasonable way to change it to get the requested results without also getting the first pair wrong.
[Answer]
A test suite. Stuff it into t/relation.t and run "prove" or "perl t/relation.t". It currently assumes the program file is "relation.rb".
It's community wiki, so feel free to add tests. If you change it, I think a timestamp (or some other obvious flag) would be in order. Wish list:
1. a "bad boy" test that will punish exhaustive search strategies
```
#
#       S. Leadley, Wed Aug 27 20:08:31 EDT 2014
use strict;
use warnings;
require File::Temp;
use File::Temp qw( tempfile tempdir );
use Test::More qw(no_plan);
# use Test::More tests => 38;
#       solution executable
my $solver='ruby relation.rb';
#       "happy" path
my $dir = tempdir( CLEANUP => 1 );
my ($fh, $filename) = tempfile( DIR => $dir );
my $testData = <<'END_TEST_DATA';
 1  ?  ? F Agatha
 2  ?  ? M Adam
 3  ?  ? F Betty
 4  1  2 M Bertrand
 5  1  2 F Charlotte
 6  ?  ? M Carl
 7  ?  ? F Daisy
 8  3  4 M David
 9  5  6 F Emma
10  ?  ? M Edward
11  ?  ? F Freya
12  7  8 M Fred
13  9 10 F Grace
14  ?  ? M Gerald
15  ?  ? F Hillary
16 11 12 M Herbert
17 13 14 F Jane
18  ?  ? M James
19 15 16 F Kate
20 17 18 M Larry
21  ? 18 F Mary
END_TEST_DATA
print $fh  $testData;
close($fh);
is( `$solver 1  2 $filename 2>&1`, "Agatha is not a blood relative to Adam.\n", 'OP example #1,  1  2');
is( `$solver 8 3 $filename 2>&1`, "David is the son of Betty.\n", 'OP example #2,  8  3');
is( `$solver 9 13 $filename 2>&1`, "Emma is the mother of Grace.\n", 'OP example #3,  9 13');
is( `$solver 4 5 $filename 2>&1`, "Bertrand is the brother of Charlotte.\n", 'OP example #4,  4  5');
is( `$solver 9 4 $filename 2>&1`, "Emma is the niece of Bertrand.\n", 'OP example #5,  9  5');
is( `$solver 5 8 $filename 2>&1`, "Charlotte is the aunt of David.\n", 'OP example #6,  5  8');
is( `$solver 16 7 $filename 2>&1`, "Herbert is the grandson of Daisy.\n", 'OP example #7, 16  7');
is( `$solver 1 9 $filename 2>&1`, "Agatha is the grandmother of Emma.\n", 'OP example #8,  1  9 (amended)');
is( `$solver 12 5 $filename 2>&1`, "Fred is the great-nephew of Charlotte.\n", 'OP example #9, 12  5');
is( `$solver 4 13 $filename 2>&1`, "Bertrand is the great-uncle of Grace.\n", 'OP example #10,  4 13');
is( `$solver 16 3 $filename 2>&1`, "Herbert is the great-grandson of Betty.\n", 'OP example #11, 16  3');
is( `$solver 6 17 $filename 2>&1`, "Carl is the great-grandfather of Jane.\n", 'OP example #12,  6 17');
is( `$solver 19 2 $filename 2>&1`, "Kate is the 3rd great-granddaughter of Adam.\n", 'OP example #13, 19  2 (amended)');
is( `$solver 1 17 $filename 2>&1`, "Agatha is the 2nd great-grandmother of Jane.\n", 'OP example #14,  1 17 (amended)');
is( `$solver 20 4 $filename 2>&1`, "Larry is the 3rd great-nephew of Bertrand.\n", 'OP example #15, 20  4');
is( `$solver 5 16 $filename 2>&1`, "Charlotte is the 2nd great-aunt of Herbert.\n", 'OP example #16,  5 16');
is( `$solver 8 9 $filename 2>&1`, "David is the cousin of Emma.\n", 'OP example #17,  8  9');
is( `$solver 19 20 $filename 2>&1`, "Kate is the 4th cousin of Larry.\n", 'OP example #18, 19 20');
is( `$solver 16 9 $filename 2>&1`, "Herbert is the cousin, twice removed, of Emma.\n", 'OP example #19, 16  9');
is( `$solver 12 17 $filename 2>&1`, "Fred is the 2nd cousin, once removed, of Jane.\n", 'OP example #20, 12 17');
is( `$solver 21 20 $filename 2>&1`, "Mary is the half-sister of Larry.\n", 'OP example #21, 21 20');
#       "sad" path
# none!
#       "bad" path
is( `$solver 1 32 $filename 2>&1`, "person with ID 32 does not exist\n", 'not required, not in the spec');
exit 0;
```
]