Working systematically

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

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?

Can you solve the clues to find out who's who on the friendship graph?

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.

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Weekly Problem 16 - 2016
How many three digit numbers have the property that the middle digit is the mean of the other two digits?

The challenge is to find the values of the variables if you are to solve this Sudoku.

There is nothing half so much worth doing as simply messing about in boats...