The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the differences to find the solution to this Sudoku.
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?
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?
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?
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.
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?
How many pairs of numbers can you find that add up to a multiple of
11? Do you notice anything interesting about your results?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the smallest number with exactly 14 divisors?
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
Can you maximise the area available to a grazing goat?
Triangle ABC is isosceles while triangle DEF is equilateral. Find
one angle in terms of the other two.
All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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.
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?
The area of a square inscribed in a circle with a unit radius is,
satisfyingly, 2. What is the area of a regular hexagon inscribed in
a circle with a unit radius?
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 spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
How many different symmetrical shapes can you make by shading triangles or squares?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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. . . .
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. . . .
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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?
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.
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?
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 is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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...
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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.
Explore the effect of reflecting in two parallel mirror lines.
Explore when it is possible to construct a circle which just
touches all four sides of a quadrilateral.
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. . . .
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Chris and Jo put two red and four blue ribbons in a box. They each
pick a ribbon from the box without looking. Jo wins if the two
ribbons are the same colour. Is the game fair?
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?