Conjecturing and generalising

problem

Gnomon Dimensions

Age

14 to 16

Challenge level

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

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

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

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

Last-But-One

Age

14 to 16

Challenge level

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
problem

Producing an Integer

Age

14 to 16

Challenge level

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

A game for 2 players
game

Jam

Age

14 to 16

Challenge level

To avoid losing think of another very well known game where the patterns of play are similar.
problem

Polycircles

Age

14 to 16

Challenge level

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?