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# Oh for the Mathematics of Yesteryear

Correct solutions were received from Mary (Birchwood Community High School) and Chor Kiang. Well done.### Part 1

### Part 2

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Age 11 to 14

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Correct solutions were received from Mary (Birchwood Community High School) and Chor Kiang. Well done.

First, find the total ounces of bread.

$600 \times35 \times24$ ounces $= 504000$ ounces

Now, find the new number of men-shares needed.

$4800 \times45 = 216000$

Divide $504000$ ounces by $216000$ to get $2\frac{1}{3}$ ounces a day.

Hence, each man must only eat $2\frac{1}{3}$ ounces of bread a day.

$ £14 10\text{s} = 290\text{s}$

$ £5 \; 8\text{s } 9 \text{d} = 108.75$ shillings

Weight (cwt) | Distance (miles) | Amount (shillings) | |
---|---|---|---|

$60$ | can be transported for | $20$ | for $290$ |

$1$ | can be transported for | $20$ | for $\frac{290}{60} = \frac{29}{6}$ |

$1$ | can be transported for | $30$ | $\frac{29}{6}\times\frac{30}{20}= 7.25$ |

$\frac{1}{7.25}$ | can be transported for | $30$ | $1$ |

$\frac{1}{7.25}\times 108.75$ | can be transported for | $30$ | $108.75$ |

Since $\frac{108.75}{7.25} = 15$

$15$ cwt can be carried for $30$ miles at a cost of $ £5 \; 8\text{s } 9 \text{d}$

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.