Project Euler Forum

I'm quite confused by the description of the game and why the example for C(5,3) is what it is. On both sides in fact--I'm confused why the four given moves are in fact winning and why there are no others. For example, for the first cut in the illustration, why can't the second player take the lower-right rectangle and cut it into four by one of the two possible ways to do so? And what distinguishes the cuts which are not in position 2 or 3 horizontally? Are they non-winning or just invalid? Maybe the root of my misunderstanding is the ambiguity of what play looks like past the first cut.... (or maybe it's not ambiguous and I'm just missing something).

I think I do maybe understand now--all four of the rectangles remain in play and either player can choose any scrap that's left to cut at any time (provided there's a valid cut to be made). That said, I will leave this thread up (a) in case anyone else has the same confusion as me (b) to make sure my understanding actually is correct and (c) to suggest that the problem could possibly use some additional illustration.

I agree, a bit confusingly the terminology "winning move" seems to be referring to a "winning opening move". That is, an opening move that forces the second player to lose no matter what they choose, rather than the final move the first player will perform before being victorious.

In general, these kinds of problems assume perfect play by the opponent. If it can lead to your victory even if the opponent plays flawlessly, it's a winning move. That said, I agree on the winning opening move part. This problem only specifies what the original paper size is, not what turn.