Working systematically

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?