Problem Teachers' Notes Hint Solution

# Lots of Lollies

Class 7Q3 at Sweyne Park School explained clearly how they solved this problem:

First of all we know it must be an odd number of lollies because there is one left over when they share by two.
Sarah noticed that 17 works as when there are only two of them they get 8 each, with one left over. But when their friends come along they get three each with 2 left over.
Danielle and Sally noticed that 7 works. Sally noticed that 27 worked, as well as 107.
So we think that any number that ends with 7 works. This is because any number that ends in 7 must be odd, and is two more than any number divisible by 5 (there are 5 friends).

It is very helpful to see how your thinking developed as you tackled this problem - thank you Class 7Q3. Poppy from Steeple Morden Primary wrote:

If the two children end up with one lolly it must be an odd number of lollies. Then 3 more children come making the total number of children 5. Say they had 1 lolly each when they shared them, the number of lollies would be seven because 1 times 5 is 5 add on 2 for the left over ones and it makes seven.
If we carry this on to 10 lollies each it shows:
1 lolly each- 7 lollies
2 lollies each- 12 lollies
3 lollies each- 17 lollies
4 lollies each- 22 lollies
5 lollies each- 27 lollies
6 lollies each- 32 lollies
7 lollies each- 37 lollies
8 lollies each- 42 lollies
9 lollies each- 47 lollies
10 lollies each- 52 lollies
You can see here that it goes up in 5s each time. The answers that are possible are the ones where the children have an odd number of lollies.
It is most probable that they will have less than 27 lollies in their bag but this is not certain they could have 5007 lollies in the bag and 1001 each leaving two left over!

Thank you Poppy. I like the way you have thought about the practical side of the problem at the end and have decided how many lollies the children are likely to have had. Phoebe and Alice from Cambridge used a 100 square to help solve the problem. Here is Alice's square:

And here is Phoebe's:

You can see that they have shaded all the odd numbers in brown and put a green cross through all the numbers that have 2 left over when shared between 5. They conclude that the number of lollies in the bag could be:

... any number that ends with a 7: 7, 17, 27, 37, 47, 57, 67, 77, 87, 97 ...

Well done both of you - you have shown how the number square is a very useful tool.