Challenge Level

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

Challenge Level

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Read this article to find out more about the inspiration for NRICH's game, Phiddlywinks.

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

Challenge Level

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Challenge Level

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Challenge Level

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

Challenge Level

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

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

Challenge Level

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

Challenge Level

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.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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.

Challenge Level

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.

Challenge Level

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Challenge Level

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Challenge Level

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

Challenge Level

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Challenge Level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Challenge Level

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Challenge Level

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Challenge Level

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

Challenge Level

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Challenge Level

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

Challenge Level

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?

Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

Challenge Level

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.

Challenge Level

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Challenge Level

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

Challenge Level

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

Challenge Level

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

Challenge Level

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Challenge Level

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

Challenge Level

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?

Challenge Level

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Challenge Level

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

Challenge Level

Use the differences to find the solution to this Sudoku.

Challenge Level

Four small numbers give the clue to the contents of the four surrounding cells.

Challenge Level

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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

Challenge Level

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?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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.