Combinations

There are 153 NRICH Mathematical resources connected to Combinations
Fruity Pairs
problem
Favourite

Fruity pairs

Age
5 to 7
Challenge level
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Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?

Mixed-up Socks
problem
Favourite

Mixed-up socks

Age
5 to 7
Challenge level
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Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
Chances are
problem
Favourite

Chances are

Age
14 to 16
Challenge level
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Which of these games would you play to give yourself the best possible chance of winning a prize?
What Shape and Colour?
problem
Favourite

What shape and colour?

Age
5 to 7
Challenge level
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Can you fill in the empty boxes in the grid with the right shape and colour?

The Twelve Pointed Star Game
problem
Favourite

The twelve pointed star game

Age
7 to 11
Challenge level
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Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
Sweets in a box
problem
Favourite

Sweets in a box

Age
7 to 11
Challenge level
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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

A City of Towers
problem
Favourite

A city of towers

Age
5 to 7
Challenge level
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In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Prison Cells
problem
Favourite

Prison cells

Age
7 to 11
Challenge level
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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?
Break it up!
problem
Favourite

Break it up!

Age
5 to 11
Challenge level
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In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Three Ball Line Up
problem
Favourite

Three ball line up

Age
5 to 7
Challenge level
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Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.