You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you work out what size grid you need to read our secret message?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
Can you complete this jigsaw of the multiplication square?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Given the products of adjacent cells, can you complete this Sudoku?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Substitution and Transposition all in one! How fiendish can these codes get?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Find the highest power of 11 that will divide into 1000! exactly.
Can you find any perfect numbers? Read this article to find out more...
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
A game that tests your understanding of remainders.
An investigation that gives you the opportunity to make and justify
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.