Math Is Fun Forum

gmsc

Member

Registered: 2008-10-05

Posts: 11

Chess Rook Addition

If I asked you to arrange the numbers 1-9, used only once each, in a 3 by 3 grid so that the first two rows add up to the 3rd, you might come up with any one of several answers. For example, you might come up with this answer:

354
618
972

This is a correct answer, because all the numbers 1-9 are used, and 354 + 618 = 972.

Let's say I instead ask you to arrange the numbers 1-9 in a 3 by 3 grid so that a chess rook, which can only move horizontally or vertically, could be placed on the number 1, and travel in sequence up to the number 9 using only legal rook moves. This is also a fairly easy puzzle, and there are several answers, including the following one:

761
852
943

In that particular arrangement, you would place the rook on the 1, move it vertically to the 2, then the 3, then do a horizontal move to the 4, move up vertically to the 5 and the 6, and then a horizontal move to the 7, which allows you to conclude by moving down vertically through the 8 to the 9.

Each of the above puzzles is fairly simple on its own, so let's make it more challenging by combining them. Can you arrange the numbers 1-9 in a 3 by 3 grid so that the top two rows add up to the third row AND so that a rook can be placed on the number 1, and moved, using only legal rook moves, to each number sequentially, and finishing on the 9?

Last edited by gmsc (2008-10-05 07:07:40)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Chess Rook Addition

I found one!

129
438
567

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Why did the vector cross the road?
It wanted to be normal.

gmsc

Member

Registered: 2008-10-05

Posts: 11

Re: Chess Rook Addition

As a matter of fact, that's the only one possible that fits both criteria!

Congrats, mathsyperson!