Working systematically

problem
LOGO challenge - following on

Age

11 to 18

Challenge level

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
problem
LOGO challenge - triangles-squares-stars

Age

11 to 16

Challenge level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
problem
LOGO challenge - sequences and pentagrams

Age

11 to 18

Challenge level

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
problem
LOGO challenge - pentagram pylons

Age

11 to 18

Challenge level

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
problem
The best card trick?

Age

11 to 16

Challenge level

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
problem
Got it

Age

7 to 14

Challenge level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
problem
Sealed solution

Age

7 to 11

Challenge level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
problem
Code breaker

Age

7 to 11

Challenge level

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
problem
Triangles to tetrahedra

Age

11 to 14

Challenge level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
problem
Penta primes

Age

7 to 11

Challenge level

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?