Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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. . . .
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Two sudokus in one. Challenge yourself to make the necessary
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you make square numbers by adding two prime numbers together?