Knight's tour

Logic Level 1

Is it possible for a Knight on a standard chess board to start at square H1 and touch every other square of the board exactly once (using standard Knight moves), finishing at square A8 ?

Yes No Not enough information to determine

2 solutions

Denton Young
Jun 30, 2017

The Knight would have to make exactly 63 moves to do this. But a Knight alternates what color square it lands on every move. KR1 and QR8 are the same color, thus the Knight can reach QR8 only on an even numbered move, not on the 63rd move.

Moderator note:

If the start and end squares are of opposite color, there will always be a path. This is true for all chessboards of even lengths and size 6 by 6 or larger.

Solution of the knight's Hamiltonian path problem on chessboards

The procedure is straightforward enough (in both the regular knight's tour where a knight returns to where it started, and the modified knight's tour with different start and end places) that mentalists have done knight tours live during shows .

Yeah! Same I thought

Aman Dubey - 3 years, 11 months ago

If it means that knight can touch any step once then it is possible to reach.1st straight twice,then left once,then straight once,then back once and at the last straight once

soumya biswas - 3 years, 11 months ago

The image shows a knight's tour to illustrate that its possible to go t every square on the board(not h1-a8). https://i.imgur.com/cUJk1RG.jpg

Siva Bathula - 3 years, 11 months ago

I have shown the Knights flight puzzle on chess tours. There are 64 squares on a chess board and so a Knight moving on move 64 will end up on exactly the same colour as the began on. So your premise that he will make 63 moves to cover every square on a chess board is incorrect. Likewise a knight to cover every square can be done in 64 moves and if you wish I can show you if you wish..

Colin Lincoln - 3 years, 11 months ago

I missed the question, but I have to disagree with Colin Lincoln. How many MOVES to cover all the squares is one less than the number of squares, even if one uses "king moves" of one space at a time. Take a sample in the lower corner . . to cover the square of four takes only three moves because the piece is already on 1H and the terminal square is black. To cover nine squares takes eight moves and the terminus is white. That smaller pattern does confirm that that 63 moves would end on a black square.

Ken Thomas - 3 years, 11 months ago

the knight have to do 6 moves to do it

Bavly Ayman - 3 years, 11 months ago

I thought the answer was not enough information because what "every other square" means, is not defined. That could mean all the white squares or all the black squares or every other spot in the path to A8 only once. I do not see the necessity of a 63 move path. "every other square" (what ever that means) allows the other half to be landed on more than once or, if it means all the white or all the black, never.

Sean Watson - 3 years, 11 months ago

Duy Anh Tran Le
Jul 15, 2017

If the start was white so the end will be black :))

But why must the end be black? Why can't it be white instead?

Pi Han Goh - 3 years, 11 months ago

if touch each square once so it has to move 63 times=> Lies on black??

Duy Anh Tran Le - 3 years, 10 months ago

Knight's tour

2 solutions

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