Solutions published for three geometrical puzzles including 'Bonnie Tiler'

The Guardian published solutions to three geometrical puzzles set earlier today.

In "Bonnie Tiler" a square grid with three corner cells missing and a three-cell straight tile raised the question of whether a 33-cell grid can be covered by 11 such tiles. The answer given is no: every orientation of the tile covers a blue, yellow and red cell, so a complete covering would require 11 cells of each colour, but the grid contains 12 red cells and 10 yellow ones.

For "Assembly needed" the left-hand shape can be cut into four identical pieces along the black lines to form a square, and the puzzle asks for a different way to cut it into four identical pieces that can be rearranged to make a square. The source lists "Solution" for this puzzle, but no solution details are provided here.

In "Pizza party" one proposed division gives three people 3/5 slices and two people 2/5 and 1/5 slices; another is to cut each pizza into five equal slices so each person gets three. The smallest number of pieces so that each person gets exactly the same numbers and sizes of pieces is given as ten pieces, with each person receiving a half and a tenth.

Thanks to Ian Stewart for the puzzles. His new book Reaching for the Extreme is out on February 12 and can be pre-ordered at the Guardian Bookshop.

Key Topics

Science, Bonnie Tiler, Assembly Needed, Pizza Party, Ian Stewart, Three Cell Tile