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## Monday, 7 April 2014

### Sunday Afternoon Maths VII Answers & Extensions

This post contains the answers to this week's Sunday Afternoon Maths and some extension problems based around the originals.

#### Ninety Nine

Every item bought will cause the pence in the total cost to fall by 1. So to spend £65.76, Susanna must have bought 24 items.
##### Extension
What is the smallest amount Susanna could spend for which we could not tell how many items she bought?

#### Reverse Bases

If ab in base 10 is equal to ba in base 4, then 10a+b=4b+a.
So, 9a=3b.
a and b must both be less than 4, as they are digits used in base 4, so a=1 and b=3.
So 13 in base 10 is equal to 31 in base 4.
By the same method, we find that:
23 in base 10 is equal to 32 in base 7
46 in base 10 is equal to 64 in base 7.

12 in base 9 is equal to 21 in base 5.
24 in base 9 is equal to 42 in base 5.
##### Extension
For which pairs of bases A and B can you find two digits g and h such that gh in base A is equal to hg in base B?