Number bases

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?

Find b where 3723(base 10) = 123(base b).

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

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.

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.

Explore a number pattern which has the same symmetries in different bases.

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

Here are many ideas for you to investigate - all linked with the number 2000.