# Clock Arithmetic and Number Theory - November 2003, Stage 4&5

## Problems

##### Age 11 to 16 Challenge Level:

If you take two integers and look at the difference between the
square of each value, there is a nice relationship between the
original numbers and that difference. Can you find the pattern
using. . . .

##### Age 14 to 16 Challenge Level:

Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine. . . .

##### Age 14 to 16 Challenge Level:

You are given the method used for assigning certain check codes and
you have to find out if an error in a single digit can be
identified.

##### Age 14 to 16 Challenge Level:

Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check. . . .

##### Age 14 to 16 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

We only need 7 numbers for modulus (or clock) arithmetic mod 7
including working with fractions. Explore how to divide numbers and
write fractions in modulus arithemtic.

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