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 arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?!
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Label this plum tree graph to make it totally magic!
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 combines all four arithmetic operations.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
A Sudoku with clues as ratios or fractions.
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
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.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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?
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?
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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. . . .
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Two sudokus in one. Challenge yourself to make the necessary
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
A Sudoku with a twist.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?