OLYMPIAD CHALLENGE 2/320: "In chess, is it possible for the knight to go (by allowable moves) from the lower left-hand corner of the board to the upper right-hand corner and in the process to light exactly once on each square?"

Question

mendicant_bias · Answer

Let's see, what are the dimensions in squares of a chess board, anyways?

jtvatsim · Answer

8x8

jtvatsim · Answer

Are the corner colors the same?

jtvatsim · Answer

That is going to be a problem I think...

jtvatsim · Answer

Lower-left is black, upper-right is black, and I believe the Knight switches colors each move.

jtvatsim · Answer

There needs to be an odd number of color switches between the first and last move. But there are 62 squares between the two corners we care about! It cannot be done!

mendicant_bias · Answer

Corner colors are the same in a diagonal, e.g. one diagonal of the board has white corner pieces at the ends, one has black. |dw:1418698015729:dw|