Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
Label this plum tree graph to make it totally magic!
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
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This Sudoku, based on differences. Using the one clue number can you find the solution?
A pair of Sudoku puzzles that together lead to a complete solution.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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.
A Sudoku with a twist.
Use the clues about the shaded areas to help solve this sudoku
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.
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 based on clues that give the differences between adjacent cells.
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with clues as ratios.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
A Sudoku that uses transformations as supporting clues.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
This Sudoku combines all four arithmetic operations.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku with clues given as sums of entries.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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 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.
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.
This Sudoku requires you to do some working backwards before working forwards.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
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.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Two sudokus in one. Challenge yourself to make the necessary
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one