Addition and subtraction

problem
Jugs of wine

Age

11 to 14

Challenge level

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
problem
Arrange the digits

Age

11 to 14

Challenge level

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
problem
Make 37

Age

5 to 11

Challenge level

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?
problem
The number crunching machine

Age

7 to 11

Challenge level

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
problem
Cinema problem

Age

11 to 14

Challenge level

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?
problem
Sept03 Sept03 Sept03

Age

7 to 11

Challenge level

This number has 903 digits. What is the sum of all 903 digits?
problem
Postage

Age

14 to 16

Challenge level

The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage stamps? Prove that all other values can be made up.
problem
1, 2, 3 magic square

Age

7 to 11

Challenge level

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
problem
Ladybirds in the garden

Age

5 to 7

Challenge level

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
problem
Got it

Age

7 to 14

Challenge level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.