Working systematically

Four small numbers give the clue to the contents of the four surrounding cells.

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

Can you find squares within a number grid whose entries add up to an even total?

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

This Sudoku, based on differences. Using the one clue number can you find the solution?

From this sum of powers, can you find the sum of the indices?

Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?