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How Many Pieces?

Age 5 to 7
Challenge Level Yellow star
  • Problem
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two knots

You can see how many loops of string were used to make these string patterns because the strings are different colours.

In the next pictures can you work out how many loops were used?

three more knots

How many pieces of string do you need to make this string pattern?

tangle of string

Can you explain how you decided?
Here is a pdf  of the string images which you could print off if you find it easier to work on paper.

If you enjoyed this problem, you might like to have a go at How Many Pieces This Time?


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Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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What is the greatest number of squares you can make by overlapping three squares?

A City of Towers

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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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