Calling all maths detectives!

Can you solve the mysteries hidden in our carefully selected NRICH tasks?
This article for Primary and Secondary teachers is all about the mathematics behind solving puzzles, unravelling mysteries and breaking codes.

Count the Digits 

Age 5 to 11 Challenge Level:
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

I Like ... 

Age 5 to 7 Challenge Level:
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Secret Number 

Age 5 to 7 Challenge Level:
Annie and Ben are playing a game with a calculator. What was Annie's secret number?

What Number? 

Age 5 to 7 Short Challenge Level:
I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

Number Detective 

Age 7 to 11 Challenge Level:
Follow the clues to find the mystery number.

Coded Hundred Square 

Age 7 to 11 Challenge Level:
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Mystery Matrix 

Age 7 to 11 Challenge Level:
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Curious Number 

Age 7 to 11 Challenge Level:
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Satisfying Four Statements 

Age 7 to 11 Challenge Level:
Can you find any two-digit numbers that satisfy all of these statements?