Working systematically

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Which of these games would you play to give yourself the best possible chance of winning a prize?

Here are two games you can play. Which offers the better chance of winning?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?