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.

Can you find a good way of recording the sequence of permutations?