Did you solve it? Are you cut out for these puzzling slices? | Mathematics
Earlier today I offered you these three geometric puzzles. Here they are again with solutions.
1. Bonnie Tiler
At the bottom left is a square grid with three of its corner cells missing. At the bottom right is a tile made up of three aligned cells.
Knowing that there are 33 cells in the grid, can you cover it with 11 of these tiles? If not, why not?
Solution No, you can’t. Each tile position covers a blue, yellow and red cell. If a covering existed, the grid would have to have 11 cells of each color. But there are 12 red blood cells and 10 yellow ones.
2. Assembly required
The left shape below can be cut into four identical pieces, cut only along the black lines, which can be reassembled to form a square, as shown in the right shape.
CHave you found a different way to cut the shape on the left into four identical pieces that can be rearranged to form a square? (Pieces can be rotated or mirrored.)
Solution
3. Pizza night
Below is a way to divide three pizzas between five people. Three people receive a 3/5 share, and two people receive a 2/5 share and a 1/5 share. Another way would be to divide each pizza into five equal slices, with each person receiving three.
What is the smallest number of coins so that each person receives exactly the same number and size of coins?
Solution Ten pieces. Each receives half a tenth.
Thanks to Ian Stewart for today’s puzzles. His new book Reaching for the Extreme is released on February 12 and can be pre-ordered from the Guardian Bookshop.
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