Solution in sight!
In the series, who better to bail out the protagonists than the »Globetrotters«: talented basketball players with brilliant scientific skills. In Bender’s body, Professor Farnsworth watches admiringly as two of the players, Sweet Clyde and Bubblegum Tate, solve the problem on a board. At the end, there is Keeler’s proof – visible to all viewers for the first time when it aired on August 19, 2010. If that’s not open source.
Keeler abstracted the problem by asking himself n presented objects that are arranged in the wrong order, such as (2, 3, 4, 5, …, ii+1, …, n, 1). The aim is to find the set (1, 2, 3, … , n) to restore by pairing the objects with two new items x and y reversed. Such a swap can be done by (i, x) note; i and x then switch positions. So you have a new set (2, 3, 4, 5, …, ii+1, …, n1, x, y).
Keeler found that one should first subdivide the set into ones ranging from 1 to i running, and another by i+1 to n goes. Then one exchanges every incorrectly placed element of the first set x and each of the second collection with y. You change at the very end x With i+1 and y with 1 out: (1, x)(2, x) (3, x)… (i, x) · (i+1, y) (i+2, y) … (n, y) · (i+1, x) · (1, y). Regardless of how you i has chosen, after these permutations one ends up with an ordered set (ignoring x and y): (1, 2, 3, … , i, i+1, …, n). In fact, it doesn’t matter how the objects were originally arranged. The method always works.
To see Keeler’s proof in action, see the Futurama episode. To do this, you first have to record the initial situation in a table in order to get an overview of who is in who’s body. In the graph, circles correspond to a person’s mind and rectangles to the exterior: