Being resilient

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Are these games fair? How can you tell?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Can all unit fractions be written as the sum of two unit fractions?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?