On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?
If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?
Can you replace the letters with numbers? Is there only one solution in each case?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
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 5?
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 identified.
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.
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.