photography > MJC

*Drum Roll... Cymbal clash*

The winner of the $35 Olympus tripod is....

EUNICE CHAN!!!!!!!!!!
since no one else joined the contest -.-

well, u identified the right step but your explanation isn't quite right.

the flaw lies in:

"When n = k + 1,
There are (k+1) horses. Remove 1 horse e.g. horse A. Then we have k horses. From assumption, the k horses have the same colour say olour 1. Replace horse B (of colour 1) in this remaining set with horse A so the number of horses is still k. From assumption, the k horses have the same colour 1. Now put back horse B and we have (k+1) horses of the same colour 1."

Now, he proof is based on ONE fundamental principle. Comparing Horse A and Horse B with the remaining k - 1 horses (let's call the set of k - 1 horses S).

So,
colour of horse B = colour of S = colour of horse A
=> they all have same colour.

Now, the proof falls apart if k - 1 = 0 i.e. when k = 2, because there is NO basis for comparison. so when k = 2, we have 2 horses, horse A and horse B. horse A is the same colour as itself, horse B is the same colour as itself and since S is empty set, there is NO COMMON colour => horses A and B may have different colours.