Working systematically

There are 604 NRICH Mathematical resources connected to Working systematically
Let's Investigate Triangles
problem
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Let's investigate triangles

Age
5 to 7
Challenge level
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Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Mixed-up Socks
problem
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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?
Counting Factors
problem
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Counting factors

Age
11 to 14
Challenge level
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Is there an efficient way to work out how many factors a large number has?
The Moons of Vuvv
problem
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The moons of vuvv

Age
7 to 11
Challenge level
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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Shopping Basket
problem
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Shopping basket

Age
11 to 16
Challenge level
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The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Three Ball Line Up
problem
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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.
Growing Garlic
problem
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Growing garlic

Age
5 to 11
Challenge level
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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Power mad!
problem
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Power mad!

Age
11 to 14
Challenge level
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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Partly Painted Cube
problem
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Partly painted cube

Age
14 to 16
Challenge level
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Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
The Puzzling Sweet Shop
problem
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The puzzling sweet shop

Age
5 to 11
Challenge level
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There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?