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Numbers are written by arranging digits in a row and each place in the row has a different value. This value depends on the base of the number system. The most common base nowadays is 10:
10x10x10x10 | 10x10x10 | 10x10 | 10 | 1 |
Ten thousands | Thousands | Hundreds | Tens | Units/Ones |
We often use these short forms for the columns:
TTh | Th | H | T | U |
To count in different bases, we just group numbers in a different way. For example, for base 2:
2x2x2x2x2x2 | 2x2x2x2x2 | 2x2x2x2 | 2x2x2 | 2x2 | 2 | 1 |
Sixty fours | Thirty twos | Sixteens | Eights | Fours | Twos | Units/Ones |
Zios count in base 3 so their numbers are grouped like this (we shall only look at the first three columns):
3x3 | 3 | 1 |
Nines | Threes | Units/Ones |
Let's work out what a Zio's 111 is in human numbers (base 10):
Nines | Threes | Units/Ones |
1 | 1 | 1 |
So, 111 = (1 x 9) + (1 x 3) + 1 = 13.
Zepts count in base 7 so their numbers are grouped like this:
7x7 | 7 | 1 |
Forty nines | Sevens | Units/Ones |
Let's see what a Zept's 111 is in base 10:
Forty nines | Sevens | Units/Ones |
1 | 1 | 1 |
So, 111 = (1 x 49) + (1 x 7) + 1 = 57.
To find out which way each type of creature is facing, calculate each number in human counting (base 10).
Remember that the creatures must be seeing numbers which could be a combination of Zios' and Zepts' legs.