Number bases

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

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?

There are two forms of counting on Vuvv - Zias count in base 3 and Zepts count in base 7. Can you work out in which direction the Zias and Zepts were looking, based on the information you're given?

You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.

How can Agent X transmit data on a faulty line and be sure that her message will get through?

Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.

A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.

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.

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

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