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

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?"

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?

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

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?

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

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?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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

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.

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

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.

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

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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?

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.

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

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?

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

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

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

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?

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

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.

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

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

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

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

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.

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?

A Sudoku that uses transformations as supporting clues.

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...

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

A pair of Sudoku puzzles that together lead to a complete solution.

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

This Sudoku, based on differences. Using the one clue number can you find the solution?

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Two sudokus in one. Challenge yourself to make the necessary connections.

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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?