Working systematically

problem

A bit of a dicey problem

Age

7 to 11

Challenge level

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
problem

Seven square numbers

Age

7 to 11

Challenge level

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
problem

Penta primes

Age

7 to 11

Challenge level

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
problem
Favourite

Counting cards

Age

7 to 11

Challenge level

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
problem
Favourite

Fitted

Age

7 to 11

Challenge level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
problem
Favourite

Symmetry challenge

Age

7 to 11

Challenge level

How many symmetric designs can you make on this grid? Can you find them all?
problem

Counters

Age

7 to 11

Challenge level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
problem
Favourite

5 on the clock

Age

7 to 11

Challenge level

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
problem

Uncanny triangles

Age

7 to 11

Challenge level

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
problem
Favourite

Triangles all around

Age

7 to 11

Challenge level

Can you find all the different triangles on these peg boards, and find their angles?