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:

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.