Iteration

problem
Slippage

Age

14 to 16

Challenge level

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
problem
Spirostars

Age

16 to 18

Challenge level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
problem
V-P cycles

Age

16 to 18

Challenge level

Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?
problem
Stretching fractions

Age

14 to 16

Challenge level

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?
problem
Peaches in general

Age

14 to 16

Challenge level

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.
problem
Triangle incircle iteration

Age

14 to 16

Challenge level

Keep constructing triangles in the incircle of the previous triangle. What happens?
problem
Dalmatians

Age

14 to 18

Challenge level

Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
problem
Difference dynamics

Age

14 to 18

Challenge level

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
problem
Archimedes numerical roots

Age

16 to 18

Challenge level

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem
Rain or shine

Age

16 to 18

Challenge level

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.