Cherries Come in Twos
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:
| 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.
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