In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
Can you work out which spinners were used to generate the frequency charts?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Can you work out the probability of winning the Mathsland National Lottery?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
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 hit?
You'll need to know your number properties to win a game of Statement Snap...
Can you find the values at the vertices when you know the values on the edges?
If you move the tiles around, can you make squares with different coloured edges?
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Explore the relationships between different paper sizes.
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
What's the largest volume of box you can make from a square of paper?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Use your skill and judgement to match the sets of random data.
There are nasty versions of this dice game but we'll start with the nice ones...
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
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 diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
Where should you start, if you want to finish back where you started?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Which set of numbers that add to 10 have the largest product?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Can you find any two-digit numbers that satisfy all of these statements?
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 make two lights switch on at once? Three lights? All four lights?