Earlier today I set you the following puzzle:
A carpenter needs a square piece of wood measuring 30 inches by 30 inches. Unfortunately the only suitable piece in his workshop is a rectangle 25 inches by 36 inches.
How does he saw the wood into two pieces, such that the two pieces can be glued together to make the square he wants?
Solution
The area of the rectangle (25 x 36 = 900) and the area of the desired square (30 x 30 = 900) are the same, which is reassuring...
After some scribbling on the back of an envelope I hope you realised that you solve it in steps:
Cut the rectangle in a zigzag, as if drawing steps with 5 inch height and 6 inch width, and the two pieces will slot together perfectly.
You were only going to solve this puzzle by scribbling around on pieces of paper, which is just what this reader from Katherine in Australia’s Northern Territory did. And he cracked it too.
I couldn’t have put the reasoning process better than reader Ryan Clark, who wrote:
Start with the self-evident principles that your 36cm sides must somehow be trimmed to 30cm and your 25cm sides need to be added to. From there you’re only a few short leaps to the answer.
I hope you enjoyed the puzzle, I’ll be back in two weeks.
I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one.
I’m always on the look-out for great puzzles. If you would like to suggest one, email me. Thats to Martin Usher for suggesting today’s.
My most recent book is Can You Solve My Problems, A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles. My children’s book Football School: Where Football Explains The World, co-written with Ben Lyttleton, was recently shortlisted for the Blue Peter Book Award 2017.
