Addition and subtraction

problem
Digit sum

Age

14 to 16

Challenge level

What is the sum of all the digits in all the integers from one to one million?
problem
Card trick 2

Age

11 to 14

Challenge level

Can you explain how this card trick works?
problem
Pair sums

Age

11 to 14

Challenge level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
problem
Have you got it?

Age

11 to 14

Challenge level

Can you explain the strategy for winning this game with any target?
problem
Birthday cakes

Age

5 to 7

Challenge level

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
problem
Domino join up

Age

5 to 7

Challenge level

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
problem
Six is the sum

Age

7 to 11

Challenge level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
problem
Butterfly flowers

Age

5 to 7

Challenge level

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?
problem
Fair exchange

Age

5 to 7

Challenge level

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
problem
The puzzling sweet shop

Age

5 to 11

Challenge level

There were cola bottles for 2p, mini eggs for 3p, marshmallow twists for 5p and lollipops for 7p in the sweet shop. What could each of the children buy with their money?