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

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.

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?

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?

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

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

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?

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

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?

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

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?

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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

A Sudoku that uses transformations as supporting clues.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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?

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?

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

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

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?

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

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

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

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

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?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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

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.

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

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

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?

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

A Sudoku based on clues that give the differences between adjacent cells.

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

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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.

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

Find out about Magic Squares in this article written for students. Why are they magic?!