Working systematically

problem
Leftovers

Age

14 to 16

Challenge level

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 $n+4$?
problem
Even squares

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
Mini Kakuro

Age

11 to 14

Challenge level

The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?
problem
Pole star Sudoku 2

Age

11 to 16

Challenge level

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

Age

7 to 11

Challenge level

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
problem
Integer indices

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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?
problem
Blockupied

Age

11 to 14

Challenge level

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
problem
Alphabetti Sudoku

Age

11 to 16

Challenge level

This Sudoku requires you to do some working backwards before working forwards.