From the Netherlands Junior Maths Olympiad:
There is a kangaroo in the centre of each square of a 5-by-5 grid of squares. Lightning strikes, and each kangaroo simultaneously jumps one square up, down, left or right. What is the greatest possible number of empty squares that could remain?
It’s here! My new book of puzzles Elastic Numbers is now available on Amazon.
I hope you enjoy solving the problems as much as I enjoyed creating them.
A PuzzleCritic Original:
There are 999 stones in a pile. Amisi and Boaz take it in turns removing either 3 or 5 stones from the pile, with Amisi going first, until no more moves are possible. The last player to make a move wins. Which player can guarantee victory?
Happy New Year! From the 2004 Georg Mohr Contest:
Find all positive integers n such that a 2n x 2n chessboard can be covered by non-overlapping L-pieces, each covering 4 squares. Rotations and reflections are allowed.
From the 1992 Irish Maths Olympiad:
Let A be a nonempty set with n elements. Find the number of ways of choosing a pair of subsets (B,C) of A such that B is a nonempty subset of C.