Working systematically

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Mandeep's watch loses two minutes every hour. Adam's watch gains one minute every hour. Can you work out what time they arrived at the airport?

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?

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Can you draw a square in which the perimeter is numerically equal to the area?

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?

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.