Amida

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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
$12345$
$21345$
$21354$
$23154$
$23514$
$32514$
$32541$
$35241$
$35214$
$35124$
$53124$