Freedom and Constraints

At first glance, these contexts might appear quite constrained, and you might think that there is not much to explore. Take the time to look deeper, and by pushing the boundaries you may discover some mathematically interesting results.

Combining Lengths link

Combining Lengths 

Stage: 3 and 4

How many different lengths is it possible to measure with a set of three rods?

Climbing the Stairs link

Climbing the Stairs 

Stage: 3 and 4

In how many ways can I get upstairs?

Going to the Cinema link

Going to the Cinema 

Stage: 3 and 4

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

You Can't Make an Omelette... link

You Can't Make an Omelette... 

Stage: 3 and 4

Can you devise the most efficient strategy for finding the highest floor from which you can drop an egg safely?