Are you ready to put your logical thinking and spatial reasoning to the test? This week's selection of puzzles comes directly from the mind of one of Britain's most celebrated and enduring popular mathematics writers, Ian Stewart.
A Trio of Geometrical Head-Scratchers
All three challenges presented today are rooted in geometry, demanding a blend of visual insight and clever problem-solving. They are perfect for a mental workout and showcase the elegant, sometimes surprising, nature of mathematical thinking.
1. The Bonnie Tiler Challenge
Your first task involves a tiling problem. Imagine a square grid that is missing three of its corner cells, leaving a total of 33 cells. You have a supply of tiles, each made of three cells in a straight line. The question is simple yet tricky: can you cover all 33 cells of this incomplete grid using exactly 11 of these three-cell tiles? If you believe it's impossible, you'll need to explain precisely why.
2. A Square Assembly Puzzle
The second puzzle is a dissection and reassembly problem. You are shown a specific shape on the left, which 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 find a different way to cut that same original shape into four pieces (which may be rotated or reflected) that will also assemble into a square.
3. The Perfect Pizza Party Division
Finally, a deliciously fair conundrum. You have three identical pizzas to share equally among five people. One method is to give three people a single 3/5 slice each, and the other two people a 2/5 slice and a 1/5 slice each. Another is to cut each pizza into five equal slices and give everyone three slices. But what is the absolute smallest number of total pieces you can cut the three pizzas into so that each person ends up with exactly the same amount of pizza, comprised of identical pieces?
Answers and A New Mathematical Journey
The solutions to these puzzles will be revealed later. In the meantime, it's worth noting that Ian Stewart, a stalwart of British science communication since the 1970s, has a new book out. Titled Reaching for the Extreme, it is described as a superlative survey of superlatives, delving into fascinating quests for the biggest, smallest, fastest, and weirdest examples in mathematics.
Published in his characteristically brilliant and clear style, the book is available for pre-order ahead of its release on February 12. While today's puzzles aren't drawn directly from its contents, they perfectly capture the spirit of curious exploration that Stewart has championed for decades.
