Suppose you have n>0 boxes in a row with an inequality sign between each adjoining pair, for example: Prove, by induction on n, that you can place the numbers 1 through n in these boxes, one per box, in a way that respects the pairwise inequalities. Thus for example, the numbers 1 through 7 could be placed in the above boxes as follows: 6 > 2 < 4 > 3 > 1 < 7 > 5