Place value

problem
The thousands game

Age

7 to 11

Challenge level

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
problem
What a joke

Age

14 to 16

Challenge level

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
problem
Multiplication magic

Age

14 to 16

Challenge level

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.
problem
How many miles to go?

Age

11 to 14

Challenge level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
problem
Composite notions

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.
problem
What an odd fact(or)

Age

11 to 14

Challenge level

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
problem
The Deca Tree

Age

7 to 11

Challenge level

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.
problem
Trebling

Age

7 to 11

Challenge level

Can you replace the letters with numbers? Is there only one solution in each case?
problem
Arrange the digits

Age

11 to 14

Challenge level

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
problem
Phew I'm factored

Age

14 to 16

Challenge level

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.