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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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.
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.
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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?
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
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.
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?
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
A Sudoku with clues as ratios.
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
Use the differences to find the solution to this Sudoku.
This Sudoku, based on differences. Using the one clue number can you find the solution?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
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.
A pair of Sudoku puzzles that together lead to a complete solution.
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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.
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?
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 use your powers of logic and deduction to work out the missing information in these sporty situations?
This Sudoku requires you to do some working backwards before working forwards.
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
By selecting digits for an addition grid, what targets can you make?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.