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. . . .
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?"
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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.
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.
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
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?
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
A Sudoku with clues as ratios.
The clues for this Sudoku are the product of the numbers in adjacent squares.
This Sudoku combines all four arithmetic operations.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
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.
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. . . .
Four small numbers give the clue to the contents of the four
Find out about Magic Squares in this article written for students. Why are they magic?!
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A pair of Sudoku puzzles that together lead to a complete solution.
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?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
Two sudokus in one. Challenge yourself to make the necessary
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku that uses transformations as supporting clues.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
This Sudoku requires you to do some working backwards before working forwards.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original 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.
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.