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

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

How many different symmetrical shapes can you make by shading triangles or squares?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

A few extra challenges set by some young NRICH members.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

You need to find the values of the stars before you can apply normal Sudoku rules.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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.

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

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

A challenging activity focusing on finding all possible ways of stacking rods.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

This challenge extends the Plants investigation so now four or more children are involved.

What happens when you round these numbers to the nearest whole number?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?