In Lucky Luke's world, the four Dalton brothers are often lined up in increasing order of height. Let us number these notorious outlaws from 1 to 4, from the shortest (Joe) to the tallest (Averell).
You can arrange them in any order you like, for example (4, 2, 3, 1). If you retain only two, they must be in either increasing or decreasing order.
Now keep three. In our example, if we set 4 aside, we are left with the sequence (2, 3, 1), which is neither increasing nor decreasing. If, however, we "forget" 2 (Jack), we are left with the sequence (4, 3, 1), in which three of the outlaws appear in decreasing order; the same is true if we omit 3 (William), giving the sequence (4, 2, 1).
Can we always extract three of the brothers in this way, in increasing or decreasing order?
