Challenge Level

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.