You could place all of them on the board. Technically, per the ISF, no piece threatens another piece unless it is adjacent to it. This includes scouts.
Per the ISF rules regarding multi-square chasing, you are correct. BTW, many of the other quiz problems posted in this thread, rely on the double chase defense, which is also not allowed per the ISF rules (but apparently not enforced in games on this site).
However, Napoleon 1er wrote in his original post (emphasis mine) that this quiz has to be interpreted as the generalization to the 8-queens puzzle to Stratego scouts.
But before we start I have 2 little preliminary quizz. You may know in chess the famous problem " How to place 8 Queens on a chess board without having any of the 8 queens threatening another one?".
On this forum the word threatening (or threaten) will mean "beeing in degree to attack, so in stratego it means a piece is threatening another one if it is placed on a directly neighbour cell (right, left, up or down), except for the scouts who can threaten from long distance horizontally or vertically as long as there is no obstacles in between.
Or if you want to be really mathematically precise: what is the independence number (the size of the maximum independent set) of the scout's graph on the Stratego board?
Similarly, there is another famous chess problem: how many queens are needed to reach every square in at most one move? This is known in mathematics as the domination number (the size of the minimum dominating set) of the queen's graph on the chess board. For the chess queen, the answer is 5; for the chess rook (which moves like the Stratego scout) the answer is 8.
In Stratego terms: what is the minimum number of scouts that have to be placed on the Stratego board so that every square can be scouted in at most one move? The answer is 8:
It is left as an exercise for the reader to count how many different permutations of the 8 scouts dominate the entire board.
Edited by TemplateRex, 27 November 2017 - 11:18 AM.