Alien Arithmetic
Suppose that on a planet in a distant galaxy there is a highly developed humanoid life form. The aliens are rather like us but on each of their hands they have only three fingers (rather than four fingers and a thumb). This means that they count in sixes rather than tens.
In an alien first school arithmetic is done with coloured bricks. A blue brick is worth six red bricks and a red brick equals six green bricks. Using Earth-style numerals we would write this sum as:
143 + 214 = 401
We call this working in base 6 and write 6 as a suffix after each number. If we need to avoid misunderstanding,
1436 + 2146 = 4016
Working in base 6 the 5 times table looks rather different.
1 x 5 = 5
2 x 5 = 14
3 x 5 = 23
4 x 5 = 32
5 x 5 = 41
10 x 5 = 50
What do you notice about the sums of the digits in the numbers 14, 23, 32...? In our usual base 10 number system which multiplication table works like this?
Division by 5 in base 6 is more of a challenge. We can even go into ‘heximals’.
24 ÷ 5 = 31/5 = 3.1111 …
Now try exploring arithmetic in other bases such as 8 or 12.
If we experiment with bases larger than ten you will have to invent extra numerals. [For work on computers in hexadecimal (base 16) the letters A, B, C, D, E, F are used for 10, 11, 12, 13, 14, 15.]
