Number bases

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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?

In 'Secret Transmissions', Agent X could send four-digit codes error free. Can you devise an error-correcting system for codes with more than four digits?

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

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

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

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

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?