Being resilient

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?

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?

Why does this fold create an angle of sixty degrees?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Can you match these calculations in Standard Index Form with their answers?

Is it possible to find the angles in this rather special isosceles triangle?

Two ladders are propped up against facing walls. At what height do the ladders cross?