Today’s puzzles are all geometrical, and all from the mind of the UK’s most enduring and eloquent popular maths writer, Ian Stewart.
1. Bonnie Tiler
Below left is a square grid with three of its corner cells missing. Below right is a tile made of three cells in a line.
Given that there are 33 cells in the grid, can you cover it with 11 of these tiles? If not, why not?
2. Assembly needed
The left-hand shape below can be cut into four identical pieces, cutting only along the black lines, which can be fitted back together to make a square, as shown in the right-hand shape.
Can you find a different way to cut the left-hand shape into four identical pieces that can be rearranged to make a square? (The pieces may be rotated or reflected.)
3. Pizza party
Below is one way to divide three pizzas among five people. Three people get a 3/5 slice, and two get a 2/5 and a 1/5 slice. Another way would be to divide each pizza into five equal slices, with each person getting three.
What’s the smallest number of pieces so that each person gets exactly the same numbers and sizes of pieces?
I’ll be back at 5pm UK with the answers. NO SPOILERS PLEASE.
Thanks to Ian for today’s puzzles. Readers – he has a new book out! Reaching for the Extreme is a superlative survey of superlatives – stories about quests for the biggest, fewest, shortest, fastest, tightest, weirdest and greatest examples of various mathematical concepts. Ian has been the UK’s ur-populariser of maths since the 1970s and his latest tome is fascinating and written in his characteristically brilliant expository style.
We tried to conjure up a puzzle based on the contents of the book but failed. So instead, please post your favourite examples of extreme things.
Reaching for the Extreme by Ian Stewart is out on February 12 and can be pre-ordered at the Guardian Bookshop.
