GOOGLE Interview Riddle - 31 Dominoes on a Chessboard - Tricky Google question
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One of the first things you notice is that every tile covers a black & white square. And this should immediately send off alarm bells if you know we just took an evenly checkered board and removed 2 of the same color from it. That's enough to prove: you can't cover the board with dominoes.
Invariants trump -simplify, solve, generalize- as this allows you to intuitively solve the problem without any further inquiry. The -400 page book- problem would be another good such example: you notice the two invariants and can immediately go about solving the problem. No further inductive proofs or other techniques required!
Cool stuff, keep them coming!
Date: 2023-11-15
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Comments and reviews: 12
Zuriah
I solved differently. Since 31 is an odd number then if the number of horizontally placed dominoes are odd then the number of vertically placed ones must be even, and vice versa. Now if we rotate this mutilated chess board by 90 degrees and then mirror it we will end up with exactly same chess board, however odd and even numbers will change places because the rotation will turn horizontal ones into vertical and vice versa and mirroring will not change anything. So we will get that the number of horizontally placed dominoes must be even and odd at the same time, which is impossible. The same will be true with the vertical ones.
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I solved differently. Since 31 is an odd number then if the number of horizontally placed dominoes are odd then the number of vertically placed ones must be even, and vice versa. Now if we rotate this mutilated chess board by 90 degrees and then mirror it we will end up with exactly same chess board, however odd and even numbers will change places because the rotation will turn horizontal ones into vertical and vice versa and mirroring will not change anything. So we will get that the number of horizontally placed dominoes must be even and odd at the same time, which is impossible. The same will be true with the vertical ones.
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Anthony
My guess: every piece occupies two adjacent squares, and adjacent squares are never the same colour. So, there would need to be the same number of squares of each of the two colours, and there are not. So (hope I am not being foolish) there will be two non-adjacent squares, and one piece, left over at the end.
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My guess: every piece occupies two adjacent squares, and adjacent squares are never the same colour. So, there would need to be the same number of squares of each of the two colours, and there are not. So (hope I am not being foolish) there will be two non-adjacent squares, and one piece, left over at the end.
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education
It would be sneaky for a company to remove opposite color squares on the chessboard to leave a solution to see if you really paid attention or just thought you-d seen the trick they were trying to test for.
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It would be sneaky for a company to remove opposite color squares on the chessboard to leave a solution to see if you really paid attention or just thought you-d seen the trick they were trying to test for.
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StoneC0ld5345
I got it down to 30 dominoes going vertically and horizontally, and one domino on a diagonal. The question does not say that all dominoes have to be horizontal or vertical, so there we go. ;)
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I got it down to 30 dominoes going vertically and horizontally, and one domino on a diagonal. The question does not say that all dominoes have to be horizontal or vertical, so there we go. ;)
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mr.
To,
Respected sir,
I like your way of explaining,
Sir, i need your help,
Sir in which software you make this animation and related stuff, please help me, please sir.
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To,
Respected sir,
I like your way of explaining,
Sir, i need your help,
Sir in which software you make this animation and related stuff, please help me, please sir.
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EM
So the answer is: yes, possible but only if we remove 2 opposite color squares, not 2 of same color. Easy, but somehow against the prerequisites. isn't it?
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So the answer is: yes, possible but only if we remove 2 opposite color squares, not 2 of same color. Easy, but somehow against the prerequisites. isn't it?
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Yakov
What about a 3x3 or 5x5 chess board. Here the opposite diagonals have different colours. Is it always possible now? (This also has an easy solution)
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What about a 3x3 or 5x5 chess board. Here the opposite diagonals have different colours. Is it always possible now? (This also has an easy solution)
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Morbius907
Cut one of the dominoes in half. Try thinking outside the box. Or at least try to think like a person who installs tiles for a living.
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Cut one of the dominoes in half. Try thinking outside the box. Or at least try to think like a person who installs tiles for a living.
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education
Good job changing it from -to stay updated with a new logic every week- to -to stay updated with a new logic puzzle every week-
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Good job changing it from -to stay updated with a new logic every week- to -to stay updated with a new logic puzzle every week-
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vc
Even if board of same color squares the same principal holds good. Since the remaining two squares are from different rows and column
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Even if board of same color squares the same principal holds good. Since the remaining two squares are from different rows and column
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David
Obviously no. There are uneven amounts of black and white squares. Each domino takes up 1 white and 1 black square.
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Obviously no. There are uneven amounts of black and white squares. Each domino takes up 1 white and 1 black square.
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Ramesh
I have been fighting since yesterday for solution, I Ignored the possibility. that answer can be just no. -
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I have been fighting since yesterday for solution, I Ignored the possibility. that answer can be just no. -
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