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Happy Octopus

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.


The number 3723(in base 10) is written as 123 in another base. What is that base?

Oh for the Mathematics of Yesteryear

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?

Base Puzzle

Age 11 to 14
Challenge Level

Here is some help if you need it.