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Cherries Come in Twos

Age 7 to 11 Challenge Level:

Abigail from Histon and Impington Infants School sent a very clear solution to this problem:

I used some counters to represent the cherries. I did what Suzie did and worked out that if you started with $4$ cherries, you would end up with $1$ left after doing pair, pair, single. If you started with $8$ cherries, you would end up with $2$. If you started with $12$, you would end up with $3$, and if you started with $16$, you would end up with $4$.
I spotted that the end numbers went up by one each time, and the start numbers went up by four. Then I did a table:

Table of results for Cherries Come in Two's!
Start End
4 1
8 2
12 3
16 4
20 5
24 6
28 7
32 8
36 9
40 10
44 11
48 12
52 13
56 14

So there were $56$ cherries in the bowl at the start.

Well reasoned, Abigail.