Working systematically

problem
Exhaustion

Age

16 to 18

Challenge level

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
problem
Magic W

Age

14 to 16

Challenge level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
problem
How old are the children?

Age

11 to 14

Challenge level

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
problem
Ones only

Age

11 to 14

Challenge level

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
problem
Master minding

Age

11 to 14

Challenge level

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?
problem
Pattern of islands

Age

11 to 14

Challenge level

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
problem
Read this page

Age

11 to 14

Challenge level

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
problem
Spell by numbers

Age

7 to 11

Challenge level

Can you substitute numbers for the letters in these sums?
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
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.