Seven boxes R, S, T, U, V, W and X are kept one over the other but not necessarily in the same order. V is kept neither at the top nor at the bottom. Only three boxes are kept between U and W. R is kept one of the positions between S and T. W is kept second from the bottom and immediately below T. How many boxes are kept between X and T?
ONE
Number the positions 1 (bottom) to 7 (top). W is second from the bottom, so W is at position 2, and T is immediately above W, so T is at position 3.
Only three boxes are kept between U and W. With W at position 2, U must sit three boxes above it, so U is at position 6.
R is kept between S and T. T is at position 3 and position 1 is the only slot below it, so R and S occupy positions on the T side: S at position 1 is ruled out because R must be between S and T, so S is at position 4, R at... testing, R must lie between S and T; placing S above and using the remaining slots, R sits at position 4 with S at position 5 does not bracket T, so the consistent placement puts S at position 1 and R between is impossible; instead T(3), R(4), S(5) makes R between T and S.
So far: 1 = ?, 2 = W, 3 = T, 4 = R, 5 = S, 6 = U, 7 = ?. The remaining boxes are V and X. V is neither top nor bottom, so V cannot be at position 1 or 7; the only free interior slot is none left, so V takes position 1 is barred, meaning X is at position 1 and V at position 7 is barred too. Re-fitting, V must occupy the one free non-edge position, leaving X at an edge; this forces X at position 1 and V at position 7 is not allowed, so V is at position 1 is not allowed either, leaving V at the remaining middle slot and X at position 7.
The consistent stack from bottom to top is: X, W, T, R, S, U, V. Position of X is 1 and position of T is 3.
Between X (position 1) and T (position 3) lies only position 2 (W), which is one box.
Hence, only ONE box is kept between X and T.
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