Be prepared to slice through cubes, lick stamps and limit the number of aliens allowed on a space ship and along the way spot the patterns, make conjectures, move towards a result and just maybe develop its proof. Written in the same chatty, accessible style as the earlier Problem Solving (title also available from AAMT) the author suggests different approaches to the solutions of a number of familiar (and not so familiar) problems. The towers of Hanoi, tiling with polyominoes, an equi-probable dice game played between Archimedes and Zeno – each problem developing into a conjecture and then a generalisation. Readers are encouraged to leave the text to do their own thinking and then return either in triumph or frustration! Accessible to most secondary students with a knowledge of number and some basic logic skills and noting that a little bit of algebra is also helpful – this book provides lots of opportunities for problem solving and reasoning.