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!
This Sudoku, based on differences. Using the one clue number can you find the solution?
Use the differences to find the solution to this Sudoku.
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.
Four small numbers give the clue to the contents of the four
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
A pair of Sudoku puzzles that together lead to a complete solution.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A Sudoku with a twist.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
This Sudoku combines all four arithmetic operations.
A Sudoku with clues as ratios or fractions.
A Sudoku with clues as ratios.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Two sudokus in one. Challenge yourself to make the necessary
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
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.
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. . . .
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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
Different combinations of the weights available allow you to make different totals. Which totals can you make?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku that uses transformations as supporting clues.
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?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku requires you to do some working backwards before working forwards.
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
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.
A Sudoku with clues given as sums of entries.
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.