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?
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?
Show there are exactly 12 magic labellings of the Magic W using the
numbers 1 to 9. Prove that for every labelling with a magic total T
there is a corresponding labelling with a magic total 30-T.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Label this plum tree graph to make it totally magic!
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Four small numbers give the clue to the contents of the four
Use the differences to find the solution to this Sudoku.
A Sudoku with a twist.
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with clues given as sums of entries.
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 sudoku requires you to have "double vision" - two Sudoku's for the price of one
Two sudokus in one. Challenge yourself to make the necessary
This Sudoku, based on differences. Using the one clue number can you find the solution?
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
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.
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This Sudoku combines all four arithmetic operations.
This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
A pair of Sudoku puzzles that together lead to a complete solution.
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.
A Sudoku based on clues that give the differences between adjacent cells.
This Sudoku requires you to do some working backwards before working forwards.
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.
Solve the equations to identify the clue numbers in this Sudoku 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?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.