This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Number problems at primary level that require careful consideration.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Different combinations of the weights available allow you to make different totals. Which totals can you make?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Given the products of diagonally opposite cells - can you complete this Sudoku?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

A few extra challenges set by some young NRICH members.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Given the products of adjacent cells, can you complete this Sudoku?

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

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?