Working systematically

Can you make the numbers around each face of this solid add up to the same total?

How many models can you find which obey these rules?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

What is the smallest perfect square that ends with the four digits 9009?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?