Exploring and noticing

problem
Egyptian rope

Age

7 to 11

Challenge level

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?
problem
Watch the clock

Age

7 to 11

Challenge level

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
problem
What's in a name?

Age

5 to 7

Challenge level

What do you notice about these squares of numbers? What is the same? What is different?
problem
Arranging the tables

Age

7 to 11

Challenge level

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
problem
What two ...?

Age

7 to 11

Challenge level

56 406 is the product of two consecutive numbers. What are these two numbers?
problem
Special 24

Age

7 to 11

Challenge level

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
problem
Highest and lowest

Age

7 to 11

Challenge level

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
problem
Prison cells

Age

7 to 11

Challenge level

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?
problem
Difference

Age

7 to 11

Challenge level

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
problem
Heads and feet

Age

5 to 7

Challenge level

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