Conjecturing and generalising

problem

Odd Differences

Age

14 to 16

Challenge level

2 out of 3

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

Janine's Conjecture

Age

14 to 16

Challenge level

2 out of 3

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. Does this always work? Can you prove or disprove this conjecture?
problem

Gnomon Dimensions

Age

14 to 16

Challenge level

2 out of 3

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
problem

Thank Your Lucky Stars

Age

14 to 16

Challenge level

2 out of 3

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?
problem

Overlap

Age

14 to 16

Challenge level

2 out of 3

A red square and a blue square overlap. Is the area of the overlap always the same?
problem

Little Difference

Age

14 to 16

Challenge level

2 out of 3

What is the value of $2015 \times 2017$ - $2016 \times 2016$?
problem

Last-But-One

Age

14 to 16

Challenge level

2 out of 3

What is the last-but-one digit of 99! ?
problem

Is There More to Discover About Four Consecutive Numbers?

Age

14 to 16

Challenge level

2 out of 3
problem

Producing an Integer

Age

14 to 16

Challenge level

3 out of 3

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?
game

Jam

Age

14 to 16

Challenge level

3 out of 3

A game for 2 players