2 days ago
Teaser 3271
Uncut Diamonds
Andrew was building a rhombus-shaped patio. He could have paved it with equilateral triangular slabs with 1ft edges, but he wanted a layout with a hexagonal slab in place of six triangular ones at various places. He considered two layouts that were symmetrical in two perpendicular directions:
Layout 1: every triangular slab touches the perimeter of the patio in at least one point.
Layout 2: each group of three adjacent hexagonal slabs encloses exactly one triangular one.
The triangular and hexagonal slabs come in boxes of 12, and Andrew chose layout 1 because he would only need a third as many boxes of triangular slabs as layout 2.
What length were the sides of the patio and how many slabs in total would be left over?
Send your solution to: The Sunday Times Teaser 3271, PO Box 29, Colchester, Essex CO2 8GZ or email The first two correct solutions opened after next Saturday each win a £20 Waterstones voucher. Open to 18+ UK & ROI residents only.
Solution to Teaser 3269
912
The winners are: J Kelly, Walsall, West Midlands; K Walne, Heighington, Lincolnshire.
