Being resilient

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Choose some fractions and add them together. Can you get close to 1?

In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?