33How many total books are kept in Stack 2 and Stack 4?

Concept: When a fixed total of items must be split into a given number of groups holding pairwise distinct, strictly decreasing positive-integer counts, the smallest possible total such a split can ever reach is obtained by taking the smallest possible distinct values 1, 2, 3, ... in order. If the actual required total exactly equals this smallest possible total, the split is forced -- no other distinct decreasing sequence can also sum to it, because any change that keeps the values distinct and decreasing can only increase the total further.

Application: Here, 10 books are split across 4 stacks with strictly decreasing, pairwise-distinct counts (Stack 1 > Stack 2 > Stack 3 > Stack 4, each at least 1). The smallest four pairwise-distinct decreasing positive integers are 4, 3, 2, and 1 -- and 4 + 3 + 2 + 1 = 10, which is exactly the required total. Since this is already the minimum possible sum for four distinct decreasing positive integers, it is the only way to reach a total of 10 books; every other choice of four distinct decreasing positive integers sums to strictly more than 10. So Stack 1 = 4 books, Stack 2 = 3 books, Stack 3 = 2 books, and Stack 4 = 1 book -- this follows purely from the book-count constraint, before even using the specific book-placement clues. Adding the two stacks the question asks about: Stack 2 + Stack 4 = 3 + 1 = 4 books.

Cross-check: The total is 4 + 3 + 2 + 1 = 10, matching the ten books given. The strict decrease from west to east holds: 4 > 3 > 2 > 1. Any attempt to raise one of these counts while keeping all four distinct and decreasing (for example 5, 3, 2, 1) pushes the total above 10, confirming 4, 3, 2, 1 is the unique valid split. The book-placement clues about History, Science, Geography, Mathematics, Psychology, Politics, Philosophy, Biology and Literature are consistent with (though not needed to derive) this stack-size split.

Result: Stack 2 and Stack 4 together hold 4 books.