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