What is the smallest number with exactly 14 divisors?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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.
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...
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
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?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
How many pairs of numbers can you find that add up to a multiple of
11? Do you notice anything interesting about your results?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G =
F and A-H represent the numbers from 0 to 7 Find the values of A,
B, C, D, E, F and H.
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .
Why does this fold create an angle of sixty degrees?
A hexagon, with sides alternately a and b units in length, is
inscribed in a circle. How big is the radius of the circle?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
A game for 2 or more people, based on the traditional card game
Rummy. Players aim to make two `tricks', where each trick has to
consist of a picture of a shape, a name that describes that shape,
and. . . .
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Think of two whole numbers under 10. Take one of them and add 1. Multiply by 5. Add 1 again. Double your answer. Subract 1. Add your second number. Add 2. Double again. Subtract 8. Halve this number. . . .
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Triangle ABC is isosceles while triangle DEF is equilateral. Find
one angle in terms of the other two.
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
Is it always possible to combine two paints made up in the ratios
1:x and 1:y and turn them into paint made up in the ratio a:b ? Can
you find an efficent way of doing this?
A decorator can buy pink paint from two manufacturers. What is the
least number he would need of each type in order to produce
different shades of pink.
Use the differences to find the solution to this Sudoku.