List

Freedom and constraints

Mathematicians often explore structures, notice patterns, find rules and make generalisations. Once they feel they understand a structure, they then push at the boundaries, change the problem, and explore the new structures that emerge.

In this feature, we have chosen some resources from the Freedom and Constraints pathway on wild.maths.org.

Here's how you can send your solutions to these problems.

13 Steps
problem

13 steps

Age
11 to 16
I wonder if there's a different way to climb 13 steps for each day of the year... Solving this problem might lead you to a famous number sequence.
Measuring with Rods
problem

Measuring with rods

Age
11 to 16
How many different lengths is it possible to measure with a set of three rods? Explore this problem, and make some discoveries about number bases.
Cinema Sweets
problem

Cinema sweets

Age
11 to 16
Charlie has 3 coins in his pocket that add up to 32p - what could they be? Come and explore this and other exciting questions about the maths of partitioning.
Heavy Pockets
problem

Heavy pockets

Age
11 to 16
In a world with just pennies, your purse or pockets would be very heavy. Two-coin systems make life much easier... Which coins would you choose?