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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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. . . .
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...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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.
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Use the differences to find the solution to this Sudoku.
Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
A jigsaw where pieces only go together if the fractions are equivalent.
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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 is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Can you work out the dimensions of the three cubes?