Reasoning, convincing and proving

problem
Digital counter

Age

14 to 16

Challenge level

When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?
problem
Digital book

Age

11 to 14

Challenge level

If it takes 852 digits to number all the pages of a book, what is the number of the last page?
problem
Multiplication magic square

Age

11 to 14

Challenge level

Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
problem
Mini cross-number

Age

11 to 14

Challenge level

Which digit replaces x in this crossnumber?
problem
The London Eye

Age

14 to 16

Challenge level

The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?
problem
Would you like a jelly baby?

Age

11 to 14

Challenge level

What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
problem
Would you rather?

Age

7 to 11

Challenge level

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
problem
Strange bank account

Age

11 to 14

Challenge level

Imagine a very strange bank account where you are only allowed to do two things...
problem
Magical products

Age

11 to 14

Challenge level

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?
problem
Perimeter possibilities

Age

11 to 14

Challenge level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?