Amida

Stage: 5 Challenge Level:

Can you prove that for every Almida framework, no two paths ever end up at the foot of the same upright? We have to show that the system described is a permutation (re-arrangement) of the numbers $1$ to $n$ which occur at the top of the uprights.

Imagine moving numbered counters down the paths at the same rate and every time a rung is encountered the two counters on adjacent uprights change places; this is called a transposition.

This is a good way of recording the sequence transpositions
$12345$
$21345$
$21354$
$23154$
$23514$
$32514$
$32541$
$35241$
$35214$
$35124$
$53124$

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. More information on many of our other activities can be found here.
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