Creating and manipulating expressions and formulae

problem
Boxed in

Age

11 to 14

Challenge level

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
problem
Legs eleven

Age

11 to 14

Challenge level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
problem
Hallway borders

Age

11 to 14

Challenge level

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
problem
System speak

Age

16 to 18

Challenge level

Five equations... five unknowns... can you solve the system?
problem
Odd differences

Age

14 to 16

Challenge level

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
problem
Fibs

Age

11 to 14

Challenge level

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
problem
Always the same

Age

11 to 14

Challenge level

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
problem
Always two

Age

14 to 18

Challenge level

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
problem
Consecutive squares

Age

14 to 16

Challenge level

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
problem
2-digit square

Age

14 to 16

Challenge level

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?