Notes from an Inspector's Notebook: July 2005

These offerings from John's notebook are an opportunity to make your own tasks.
I was reminded of the Glaeser's dominoes when Kath Cross (another retired inspector) introduced the problem below at a recent ATM workshop in Leicester.

CHESS BOARD PROBLEMS

Take a chess board and a set of 32 dominoes, of matching size! It is relatively easy to see that the board can be completely covered by the dominoes.

What happens if two squares are removed from opposite corners of the board?

  • Can 31 dominoes cover the board?
  • AND SO ON!
Suppose that the two squares removed are not in opposite corners - what happens then?

Under what circumstances can 31 dominoes cover the board?

As a young teacher of mathematics I collected problems and kept them in what I called a commonplace book. I used this book as fill-ins: for kids who had finished, homework, starters, mains and the rest. It contained one of my all time favourite puzzles about dominoes but the book was lost. Many years later I found the puzzle on a poster at the then West London Institute of Higher Education. So the puzzle again found a place of honour in my inspector's notebook.

GLAESER'S DOMINOES

George Glaeser of Strasbourg put a set of dominoes, more or less randomly, in a flat tray and took a photograph. The exposure was not correct, and although the numbers could be discerned, the positions of the dominoes could not. 
3  6  2  0  0  4  4
6  5  5  1  5  2  3
6  1  1  5  0  6  3
2  2  2  0  0  1  0
2  1  1  4  3  5  5
4  3  6  4  4  2  2
4  5  0  5  3  3  4
1  6  3  0  1  6  6

Can you reconstruct the dominoes?

John Hibbs
19 July 2005

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