Three Spinners
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Problem
This is a number spinner. When you spin it, it can land on any number from one to ten.
Here are three more number spinners with ten numbers on them. But you cannot see what the numbers are.
I spun the red one $15$ times and got these numbers:
I spun the blue one $15$ times and the yellow one $15$ times and got these numbers:
Then I did the same things again twice over. I got these numbers, but forgot to note which numbers came from which spinner:
Can you work out which spinner generated each list? How did you do it?
We could call the numbers on the first spinner "Numbers from one to ten".
Can you think of a title for the set of numbers on the red spinner?
Can you think of titles for the sets of numbers on the blue and the yellow spinners?
Getting Started
What do the numbers on each card have in common with each other?
Can you see another card or cards with some of the same numbers?
Student Solutions
Andrew from Quarry Bay School sent us an image to show which numbers had come from each spinner:
Jake from Seaford Primary described how he tackled this problem:
First I wrote down all the numbers from the red list starting with the smallest. All the numbers were in the $2$ times table so I wrote the list again with the missing numbers in.
Then I did the same with the blue and yellow list.
I looked at the other six lists. Some had only $2$ times tables so I said they were from the red spinner. Some had only $3$ times tables so I said they were from the yellow spinner. Some had only odd numbers so I said they were from the blue spinner.
Ellie did a similar thing:
First of all I wrote down all the numbers you knew were on the red, yellow and blue spinners, as in the tables.
I then checked these over with the tables with no matching colours and saw which ones fitted each.
I filled in the missing numbers which were not in the first three tables and came up with $10$ numbers for each colour and titles as well.
RED - even numbers from $0$ to $18$
BLUE - odd numbers from $1$ to $19$
YELLOW - multiples of three from $0$ up to $27$
Well done also to Jonathan from New Ford Primary, children from Stourport Primary and pupils from Dr Challenor's Grammar School who all sent very clear explanations of the ways they solved this problem.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.