Try Playing 1729 Moves Backwards

Logic Level 1

A single knight is placed on a certain square of a standard chess-board. After performing 1729 moves, it arrives at a white colored square. What was the color of the square on which the knight was initially on?

White Black Insufficient information

1 solution

Nihar Mahajan
May 3, 2016

Relevant wiki: Chess Puzzles

Label black color as $B$ and white color as $W$ . We know that a knight moves in L shape, that is, it will travel through $BWBW$ or $WBWB$ per move.So after every move, the knight lands on the square opposite in color of the square it was initially on. If we consider the color of square after $n^{th}$ move, we get the two sequences:

If initial color was white we have: $B,W,B,W,B,W,\dots$

If initial color was black we have: $W,B,W,B,W,B,\dots$

Note that if the initial color was black, we have white at odd number in the sequence and in the problem after $1729$ moves i.e odd moves, the knight arrives at white colored square, so the initial square it was standing on was black in color.

Moderator note:

Good observation about the parity of knight moves.

I really think you implemented 1729 because it was a taxicab number.

Mohammad Farhat - 2 years, 8 months ago

Try Playing 1729 Moves Backwards

1 solution

Moderator note:

0 pending reports