How Many Pieces?
1 out of 3
How many loops of string have been used to make these patterns?
Problem
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?
How many pieces of string do you need to make this string pattern?
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?
Getting Started
What happens when you choose a starting point and follow the string from there?
You could print off this picture of the patterns and use a pencil to follow a loop.
Student Solutions
Thank you to everyone who sent in a solution to this problem. Most of you agreed that there was just one piece of string in the first picture, two in the second, one in the third and two in the fourth.
Thomas from St Luke's School in Frodsham explained how he worked out the number of pieces of string in the last picture:
I started at one point, followed the string round in one direction and found that I came back to where I started. I realised that I hadn't been everywhere, so I started from a place that I hadn't been and went around again. When I got back to the start again, I had been everywhere, so there are two loops.
This is very clear - thank you Luke.
Well done also to Diana, Kate and Georgia from Danebank School who also wrote clear explanations of how they counted the pieces of string.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Key questions
Possible extension
Learners could go on to How Many Pieces This Time?
Possible support
Suggest using this sheet to follow round the pieces of string with a coloured pencil.