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Results tagged with checkerboard
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user 16478
A puzzle involving checkerboards: grids of squares alternating black and white in color, most commonly an 8x8 board.
3
votes
Professor Halfbrain's infinite chessboard theorems
Theorem 1a is also true and it 'follows' from the previous result. Suppose we have colored our infinite chessboard blue and red, and suppose without loss of generality the red squares are not queen-co …
- 2,567
12
votes
Professor Halfbrain's chessboard theorems
Adding to Joe Z.'s answer, the third theorem is also false.
2 1 1 3
1 3 1 2
1 1 3 2
3 2 2 1
The the bottom-right 1, the top-left 2 and the middle 3's (versus the outer 3's) are …
- 2,567
10
votes
Accepted
Professor Halfbrain and the 9x9 chessboard (Part 2)
I've been thinking on this problem for a long time, and I think I nailed it. I will expand on the ideas I used for the solution of part 1 of this puzzle, and also on the reasoning of Michael Seifert's …
- 2,567
16
votes
Accepted
Professor Halfbrain and the 9x9 chessboard (Part 1)
There is a simple way to see that manshu's answer $x=25$ is correct.
Translate the problem into an easier problem:
Rather than consider a $9\times 9$ board and pawns, consider a $10 \times 10$ board a …
- 2,567
8
votes
Accepted
Concentrating tokens on an infinite board
Following in the footsteps of Big Black Box's and Trenin's answers, this shows very concretely that...
I tried a lot of different approaches to this problem, but ultimately it's taking the courage …
- 2,567