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.
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?
Four small numbers give the clue to the contents of the four surrounding cells.
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.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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.
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.
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?
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?
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
A Sudoku with clues as ratios or fractions.
Two sudokus in one. Challenge yourself to make the necessary connections.
A Sudoku based on clues that give the differences between adjacent cells.
Given the products of diagonally opposite cells - can you complete this Sudoku?
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
A Sudoku with clues as ratios.
A Sudoku with a twist.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A pair of Sudoku puzzles that together lead to a complete solution.
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
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.
This Sudoku combines all four arithmetic operations.
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.
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?
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?
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?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Sudoku with clues given as sums of entries.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Solve the equations to identify the clue numbers in this Sudoku problem.
A Sudoku with a twist.
An introduction to bond angle geometry.
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?
This Sudoku requires you to do some working backwards before working forwards.