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

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

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

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

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?"

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

What happens when you round these three-digit numbers to the nearest 100?

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

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Have a go at balancing this equation. Can you find different ways of doing it?

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?

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?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Can you work out some different ways to balance this equation?

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

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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

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

Use the differences to find the solution to this Sudoku.

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?

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?

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.

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?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

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

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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

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?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?