Number bases

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 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 - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of the creatures they could see. The creature looking to the West wrote 122. The creature looking to the East wrote 22. The creature looking to the South wrote 101. The creature looking to the North wrote 41. In which direction are the 2 Zios looking and in which directions are the 2 Zepts looking?

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.

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

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.

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.

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?