Freedom and Constraints
How Much Can We Spend?
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?
Largest Product
Which set of numbers that add to 100 have the largest product?
Perimeter Expressions
Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
Cinema Problem
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
What Numbers Can We Make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Gabriel's Problem
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
American Billions
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 Numbers Can We Make Now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Peaches Today, Peaches Tomorrow...
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Weights
Different combinations of the weights available allow you to make different totals. Which totals can you make?
1 Step 2 Step
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?
Take Three from Five
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Two and Two
How many solutions can you find to this sum? Each of the different letters stands for a different number.