Today’s challenge consists of three geometrical puzzles crafted by Ian Stewart, a leading UK-based popular mathematics writer. These puzzles explore concepts of tiling, dissection, and fair division, pushing logical thinking in accessible ways.
Puzzle 1: Bonnie Tiler
The first puzzle involves a 33-cell grid with three corner cells missing. The question is whether it can be fully covered with 11 tiles, each consisting of three connected cells in a line. The answer is no. This is because the missing corners create an imbalance in the grid’s geometry. A grid with 33 cells cannot be tiled by groups of three without leaving gaps or overlaps. The missing corners introduce asymmetry that makes a complete tiling impossible.
Puzzle 2: Assembly Needed
This puzzle presents a shape that can be dissected into four identical pieces, which then reassemble into a square. The challenge is to find an alternative way to cut the shape. While many solutions exist, the key lies in identifying the symmetry within the original shape. This puzzle highlights how the same form can be broken down and reconstructed in multiple ways, illustrating principles of geometric transformation.
Puzzle 3: Pizza Party
The final puzzle explores fair division among five people using three pizzas. One solution involves uneven slices (3/5, 2/5, and 1/5), but the puzzle asks for the smallest number of pieces needed to ensure everyone receives equal portions. The most efficient solution is to divide each pizza into five equal slices, giving each person three. This puzzle demonstrates that equal distribution doesn’t always require equal-sized slices; the total amount matters more than the individual cut.
Beyond the Puzzles: Stewart’s New Book
Ian Stewart’s latest book, Reaching for the Extreme, provides a fascinating look at mathematical superlatives. From the largest prime numbers to the shortest paths, the book delves into the boundaries of mathematical concepts. Stewart has long been influential in popularizing mathematics, making complex ideas accessible without sacrificing rigor. The book is a testament to his skill in explaining extreme mathematical phenomena in a compelling way.
These puzzles and Stewart’s work remind us that mathematics isn’t just about calculations; it’s about logic, symmetry, and the elegant solutions hidden within complex problems.
