Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
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. . . .
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
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.
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?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Given the products of adjacent cells, can you complete this Sudoku?
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.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve 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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
A pair of Sudoku puzzles that together lead to a complete solution.
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
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
Two sudokus in one. Challenge yourself to make the necessary
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku based on clues that give the differences between adjacent cells.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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.
This Sudoku combines all four arithmetic operations.
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.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
Four small numbers give the clue to the contents of the four
A Sudoku that uses transformations as supporting clues.
This Sudoku requires you to do some working backwards before working forwards.
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.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Solve the equations to identify the clue numbers in this Sudoku problem.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?