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Steel Cables

Age 14 to 16
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Steel Cables printable worksheet
 

Cables can be made stronger by compacting them together in a hexagonal formation.

Here is a 'size 5' cable made up of 61 strands:

How many strands are needed for a size 10 cable?

How many for a size n cable?

Can you justify your answer?


Once you've had a go at the problem, click below to see the diagrams some students produced when they worked on it.
Do these diagrams give you any ideas for how you could work out the number of strands needed?

Group 1

student's picture of hexagon split into three quadrilaterals, two 5*5 rhombuses and a 4*4 rhombus

Group 2

student's picture of cable with horizontal arrows showing row lengths n, n+1, n+2 up to 2n-1 in the middle and then decreasing back down to n

Group 3

student's picture of hexagon split into six triangles

Group 4

student's picture of hexagon showing four rings and one cable in the centre


The work that these students did using their diagrams is given on the Getting Started page, if you would like another hint.


Which of the four approaches makes the most sense to you?
What do you like about your favourite approach?

Can you think of any other approaches?

Notes and Background

Hexagonal packings are often chosen for strength or efficiency. To read more about packings, take a look at the Plus articles Mathematical Mysteries: Kepler's Conjecture and Newton and the Kissing Problem

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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