Being resilient

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.