Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
What are the last two digits of 2^(2^2003)?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
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. . . .
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. . . .
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
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. . . .
A composite number is one that is neither prime nor 1. Show that
10201 is composite in any base.