Earlier today, I shared a perplexing puzzle with you about an object that can pass through a small hole but not a big one. Let’s revisit the puzzle and explore the solutions.
Imagine designing an object that cannot pass through an open window but can pass through a window that is nearly closed. To help visualize this, consider a window with two casements – one on each side. When both casements are fully open, the object cannot pass through. However, when one of the casements is almost closed, the object can pass through.
To achieve this, the object needs to curve around the partially closed casement. Three shapes that meet these criteria are a square with three sides, a V-shape, and a C-shape. These shapes can be seen passing through the window in illustrations and videos provided by Kvantik, a Russian math magazine for schoolchildren.
The simplest shape, a three-sided square, can curve around the closed casement and pass through the window. The V-shape and C-shape also demonstrate this concept effectively. The C-shape, in particular, is quite elegant in its design.
If you’re up for a challenge, you could calculate the precise dimensions of these shapes in relation to the window width, casement thickness, and angle of the partially shut casement. Feel free to share your findings in the comments below.
I would like to express my gratitude to Kvantik for sharing today’s puzzle with us. Additionally, I am excited to announce that my new book, “Think Twice,” will be released on Thursday. This book features a collection of counterintuitive puzzles along with explanations of why they often deceive us. If you enjoyed today’s puzzle, I believe you will find the book captivating.
“Think Twice: Solve the simple puzzles (almost) everyone gets wrong” is available for order at guardianbookshop.com to support the Guardian and Observer. Delivery charges may apply.
Since 2015, I have been presenting puzzles here on alternate Mondays and am constantly seeking out new and engaging challenges. If you have a puzzle suggestion, feel free to email me. Thank you for joining me on this puzzling journey.