A is CORRECT. M always goes with F. If M is with I, that means FM goes on the middle shelf.
In the setup, we saw that placing FM on the middle shelf determined everything:
This is what the diagram looks like if FM are on the bottom shelf instead:
If FM are on the bottom shelf, this game is almost impossible to lock down. There’s one more book to place: the 8th book can go on shelf three or four.
None of the remaining answers deal with this. Answers B, C and E place one of the random variables, G and H. That really doesn’t do much in this game.
K and G (answer B) and H and O (answer E) could both go together on either the top or the middle shelf. They’re very easy to move around, if F and M are on the bottom shelf.
If F, H and M are all on the bottom (D), we still get to decide whether we want to put a fourth book on the bottom, or put a third book on the middle shelf.
The same is true of C. If you put L and F together, they go on the bottom. M goes there too, with F. You still get to decide whether to put a fourth book with them, or a third book on the middle shelf instead.
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