Okay were going down this path now......

Statement: All horses are the same colour.

Proof (by induction): For one horse the statement is true. assume the statement is true for any set of k horses, then consider a set of k+1 horses.

then take any two distinct k element subsets

and

for example. we know that all the horses in the k element subsets are the same colour, so

and

. this gives

. so this prove that for any set of k+1 horse they are the same colour. so by induction all horses are the same colour.

Bobak