by Des MacHale
Published: 3 July 2016 (link)
I made Jack a jigsaw. I started with a rectangle of card that I had cut from an A4 sheet and then I cut the rectangle into pieces. There were some square pieces of sizes (in centimetres) 1×1, 2×2, 3×3 … with the largest having side equal to Jack’s age. The remaining pieces were rectangles of sizes 1×2, 2×3, 3×4, … with the largest length amongst them again being Jack’s age. Then Jack succeeded in putting them together again to form a rectangle, but the perimeter of his rectangle was smaller than the perimeter of my original rectangle.
What were the lengths of the sides of my original rectangle?