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Number Detective

Follow the clues to find the mystery number.


There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?

Great Granddad

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

Magic Crosses

Age 7 to 14
Challenge Level
Here are pictures of two crosses:


What do you notice about the two crosses?
What is the same?
What is different?

Both crosses use the digits 1, 2, 3, 4, and 5.
The left cross has a horizontal total of 12 and a vertical total of 6.
The right cross has a horizontal total of 8 and a vertical total of 8.

We call the cross on the right a magic cross, because its horizontal total is equal to its vertical total.

Can you find any more magic crosses using the digits 1, 2, 3, 4 and 5?
Can you find all the possibilities?
Can you convince yourself you have found them all?

You may wish to use the Magic Cross Tester to try out your ideas.

Here are some questions you might like to consider:

Are there any magic crosses that use the numbers 2, 3, 4, 5, 6?
Or 3, 4, 5, 6, 7?
Or 98, 99, 100, 101, 102?

How many magic crosses can you find with the number 50 in the middle?

What if the numbers went up in 2s instead?
Or 3s?
Or 10s, or 20s, or 100s?

Perhaps you have some questions of your own that you would like to explore too!