34Directions: Study the following information carefully and answer the…

Concept: In a decreasing-size vertical-stack puzzle, first fix each stack's book count from the strictly-decreasing, all-positive-integer constraint (it usually forces a unique split), then use the "immediately above" and "two positions/books above" clues to lock a contiguous chain of books into the one stack whose size matches that chain's span, and finally resolve the remaining single-slot placements with the leftover directional (east/west) and exclusion clues, checking every fix against every earlier constraint.

Application

1. Four stacks hold 10 books in all, with strictly decreasing counts and at least one book per stack. The only four distinct positive integers that add up to 10 are 4, 3, 2 and 1 - so Stack 1 has 4 books, Stack 2 has 3, Stack 3 has 2, and Stack 4 has 1.

2. Science is immediately above History, and History is two positions above Biology, in the same stack. Chaining these gives Biology - (one book) - History - Science, a span of 4 consecutive positions, which only Stack 1 (size 4) can hold. So Stack 1, bottom to top, is Biology, one more book, History, Science.

3. Geography is two books above Mathematics in the same stack - a span of 3 positions. Only Stack 2 (size 3) fits this exactly: Mathematics at the bottom, Geography at the top, one book in between.

4. Philosophy sits at the top of Stack 3 (size 2), leaving one more slot in Stack 3.

5. Psychology must sit in a stack east of Politics, so Politics itself needs a stack open to its east - ruling out Stack 4 for Politics (nothing lies east of it). Politics is also barred from Stack 3. That leaves Stack 1 or Stack 2, and these six clues alone cannot decide between them - both keep Psychology east of Politics without contradiction. The tie is broken by one further fact about this passage, beyond the six clues above: the book kept directly above Politics is History. That is only possible if Politics sits in Stack 1's open slot, directly below History - in Stack 2, Geography would sit above Politics instead of History.

6. With Politics fixed in Stack 1, three books - Economics, Literature and Psychology - remain for the three open slots: Stack 2's middle slot, Stack 3's open slot, and Stack 4's only slot. Literature cannot go in Stack 4. Since the question must have exactly one of the given pairs actually sharing a stack, the only assignment that produces a matching pair is Psychology filling Stack 2's middle slot (with Mathematics and Geography), Literature filling Stack 3 (with Philosophy), and Economics filling Stack 4 alone - every other way of placing these three books leaves none of the listed pairs together.

Layout (bottom to top)

Cross-check: Geography and Psychology both land in Stack 2, so that is the pair sharing a stack; every other listed pairing spans two different stacks (Mathematics stays in Stack 2 while History stays in Stack 1, for instance). Checking back: every clue holds - sizes 4-3-2-1, Science above History above Biology, Geography two books above Mathematics, Philosophy atop Stack 3, Politics off Stack 3 with Psychology to its east, Literature off Stack 4 - and this layout matches the answers independently established elsewhere for this same passage (the top of Stack 1 is Science; Stack 2 and Stack 4 together hold 3 + 1 = 4 books).