Are you ready for a mental workout? This week's selection of puzzles comes directly from the mind of one of the United Kingdom's most celebrated and enduring popular mathematics writers, Ian Stewart. The three geometrical conundrums are designed to stretch your logical and spatial reasoning.
A Trio of Brain-Twisting Challenges
The puzzles presented today all involve shapes, patterns, and fair division. They are classic examples of the kind of elegant, thought-provoking problems that have made Stewart a household name among puzzle enthusiasts for decades. Your task is to find the solutions through clever thinking, not brute force.
1. The Bonnie Tiler Conundrum
The first puzzle presents a square grid with a twist: three of its corner cells are missing. This leaves a shape containing 33 cells in total. You are given a tile made of three cells in a straight line. The question is straightforward yet tricky: can you cover the entire 33-cell grid with exactly 11 of these three-cell tiles? If you believe it's impossible, you must explain precisely why no such tiling exists.
2. A Square Assembly Problem
For the second challenge, you are shown a specific shape on the left. It is already known that this shape can be cut into four identical pieces by cutting only along the printed black lines. These four pieces can then be rearranged to form a perfect square, as demonstrated. Your mission is to discover a different way to cut the same left-hand shape into four pieces (which may be rotated or reflected) that will also assemble into a square. The cuts must still follow the black lines.
3. The Perfect Pizza Party
The final puzzle is a delicious problem of fair division. Imagine you have three identical pizzas to share equally among five people. One method is to divide each pizza into five equal slices, giving each person three slices. Another method, illustrated, gives three people a single 3/5 slice and two people a combination of a 2/5 slice and a 1/5 slice. The challenge is to find the method that uses the absolute smallest number of total pieces, while ensuring every person ends up with exactly the same amount of pizza in terms of both the number and the sizes of their pieces.
Celebrating a Mathematical Mind
These puzzles serve as a fitting tribute to Ian Stewart's latest literary offering. His new book, titled 'Reaching for the Extreme', publishes on February 12. Described as a superlative survey of superlatives, it delves into fascinating stories about quests for the biggest, smallest, fastest, and weirdest examples within various mathematical concepts.
Stewart has been the UK's pre-eminent populariser of mathematics since the 1970s, and this latest tome is noted for its characteristically brilliant and clear expository style. While the Guardian's puzzle column attempted to devise a new puzzle based on the book's contents, they instead invite readers to share their own favourite examples of extreme mathematical phenomena.
Answers to today's three geometrical puzzles will be revealed at 5pm UK time. Until then, readers are asked to avoid posting spoilers so everyone can enjoy the challenge. Good luck!
