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ANSWER:
The life of a space smuggler is tough. The officers of S.Q.A.T. are constantly on your tail. You have to think fast and act faster. Your ship is nearly full and you have one last pickup. You can most likely only choose one of five pickups but your contact has not seen the loads and knows nothing about them. He does know that they do each have a weight. You want to choose the one that will fit best in the ship but your contact only tells you the following:
1. Load A is equal to load C if and only if load E is not equal to B.
2. Only if load C is as much less than load B as B is less than A, is A greater than load D.
3. C is less than A and greater than D.
What is the order of magnitude of the loads so you can choose the proper load for the ship?
Solution
Per 1, if load E is not equal to load B, then A = C and if A = C, then E is not equal to B.
Per 2, if A > D, then (B – C) = (A – B).
Per 3: A > C > D. If A > D, then (B – C) = (A – B) (both are positive, since A > C). Thus, A > B, and B > C.
From the first point above, if A is not equal to C, then E = B. But we know that A is not equal to C, therefore E = B.
Order of magnitude is then:
A
B,E (B = E)
C
D
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