A game in which players take it in turns to choose a number. Can you block your opponent?
Data is sent in chunks of two different sizes - a yellow chunk has
5 characters and a blue chunk has 9 characters. A data slot of size
31 cannot be exactly filled with a combination of yellow and. . . .
I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Given the products of adjacent cells, can you complete this Sudoku?
Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
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?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Can you find any perfect numbers? Read this article to find out more...
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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...
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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?
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. . . .
Can you find a way to identify times tables after they have been shifted up?
A game that tests your understanding of remainders.
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.
Explore the relationship between simple linear functions and their
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the 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.
Substitution and Transposition all in one! How fiendish can these codes get?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Have you seen this way of doing multiplication ?
Can you work out what size grid you need to read our secret message?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Find the highest power of 11 that will divide into 1000! exactly.
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =