Being resourceful

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?

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?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

How many winning lines can you make in a three-dimensional version of noughts and crosses?