US
On alternate Friday afternoons we are posting cryptic questions from 7city Learning. Add your answers in the comments box at the bottom of the page. Approbation will be given to the person who provides the correct answer first. We’ll add the official answer to the bottom of this article on Monday afternoon.
You have a traditional chessboard, eight by eight square.
From a single diagonal, any diagonal, you remove two squares.
The board now has just 62 squares.
You also have 31 domino tiles, each of which is conveniently the same size as two of the chessboard squares.
Is it possible to cover the board with these dominoes?
Haha
No its not.
The chessboard has now 30 white squares and 32 black or 32 white and 30 black. Lets say 30 white squares and 32 black to simplify.
Every time you put a domino on the chess board (whereever you put it) you get rid of 1 white square and 1 black square.
Sot after putting 30 dominos you will have 0 white square left, 2 black squares left . These two black squares cant be next to each other excpet if they are on the same diagonal (bcause they have the same color). Therefore you cant cover these last two squares with the last domino…
No!
All squares on a diagonal have the same color. You have 32 squares of one color and 30 of the other color. A domino covers two adjacent squares that have opposite colors. You can cover at most 60 of the remaining 62 squares (with 30 dominos). Two non-adjacent squares of the same color remain.
It can’t be done. A domino would have to cover one white and one black square. Because you remove 2 squares of the same colour, ie from a diagonal, the dominos therefore won’t be able to cover the remaining squares.
Yes! But its awfully more difficult to describe how in words. Here it goes…
Start from a black square corner and remove the nearest two white diagonal squares. That black corner square will shift to become a neighbour to another black square. So this give a configuration of 7 tiles in that row, and also the row above it.
The configuration of the board can be broken into two segments
1) 6×8 – which requires 24 domino tiles
2) 2×7 – which requires 7 domino tiles
Total: 31 domino tiles
hooker stop embarrassing yourself with this nonsense, it can’t be done as the first guy said and as simple googling will reveal. Wish 7city could come up with original interesting problems instead of widely published stuff from days of yore.
No.
No. Imagine the case that the chessboard is covered with dominoes BEFORE the squares are removed.
Now the question is equivalent to asking if I can remove a single domino by removing two diagonal squares.
Its obvious that I can because however I have covered the board no domino can be oriented diagonally.