Steph

OK then. We have ten fingers, (well I do anyway). Because of this we put every column of numbers as a new multiple of 10. You remember all that hundreds, tens and units stuff? Good.

Now imagine you live in a world where people have thirteen fingers, (six and seven, I suppose). Then instead of counting in hundreds, tens and units, you'd count in 169s, 13s and units. So there'd be 14 digits:
0,1,2,3,4,5,6,7,8,9,a,b,c (a=10 in base 10, b=11, c=12). So the first 26 numbers would go as follows:

1
2
3
4
5
6
7
8
9
a
b
c
10
11
12
13
14
15
16
17
18
19
1a
1b
1c
20

For example, '20' means 2 13's and 0 units, so 20 (base 13)= 26 (base 10). Furthermore, after 99, and then 9a, 9b, and 9c, we'd finally reach a0 [presumably not known as 'a-ty' because that would just be plain confusing].

So, finally, consider doing the product 6x9 in Base 13. The result would be 5 tens and 4 units, (what we'd call '54'). If you're in Base 13, it's 4x13=52 and 2 units.

So in base 13, the formula '6x9=42' is correct. It's like binary, which is base two.

That will certainly check to see if you're reading thoroughly.

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