Working Systematically - Upper Secondary

Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

What's Possible?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

A Long Time at the Till

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

Sortedlive

Stage: 5 Challenge Level: Challenge Level:1

How can you quickly sort a suit of cards in order from Ace to King?

Adding Machine

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you set the logic gates so that this machine can decide how many bulbs have been switched on?

Ante Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Use cunning to work out a strategy to win this game.

Stage 5 Cipher Challenge

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?