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Bean Bags for Bernard's Bag

Age 7 to 11
Challenge Level

We did not have any solutions sent in for this activity, maybe it was done very practically and not much was recorded. The recording is not always the most important aspect of a piece of mathematics.

However, we would still love to hear from you if you have worked on this problem. Teachers, you may like to send in a summary of your pupils' work. Please email us:

But a little time on and we got this reponse - thank you.

We are Dominic and Sam (year 5) from St Nicolas CE Junior School, Newbury.

We noticed that you had no solutions last month to this problem, so here is our solution.

We started with 2 hoops, red and blue. We had 6 bean bags in the red hoop and 4 in the blue. We worked out that we had to add the number of bags in each together and subtract the number of bags to get 2, which is the number of bags that go in the middle (where the hoops overlap). Then if there are 6 in the red hoop, 2 are in the middle so 4 are not in the middle.

On the other way, if there are 4 in the blue, 2 are in the middle and 2 are not. For 3 hoops, we had 0 in the middle first and then 1 in the middle, next 2 and lastly 3. This way we didn't have two solutions the same. We worked out 14 solutions and we think we found them all.


From James Dixon Primary School in Bromley in March 2013

Hi its James Dixon Primary School here.  Well we found 5 different solutions to Dominic and Sam. At first we thought we had the same results because our maths group also found 14 solutions, but we were mistaken. We only had 9 the same as them and five different ones.  That means together with St Nicholas School we have found 19 solutions!
Here are our other 5 solutions.

Written by Farrah and Kieran on behalf of the Year 5 Aspen class Wednesday maths group.
Extra five solutions written out by Inthujan and Sowkhaetul

Thank you James Dixon School for these extra solutions, well done.