Box Arrangement Constraints

We have 7 boxes stacked vertically. Key conditions include:

• Four boxes between R and S (R and S are 5 positions apart).
• Three boxes between Q and T (Q and T are 4 positions apart).
• Two boxes between S and U (S and U are 3 positions apart).
• V is above P, but not immediately (V >= P + 2).
• Q is above V (Q > V).

Determining Arrangement: S, U, R

From '2 boxes between S and U' and '4 boxes between R and S':

• A possible valid setup is S at position 1, U at position 4, and R at position 6.

This fixes:

• S = Position 1
• U = Position 4
• R = Position 6

Remaining positions: {2, 3, 5, 7}. Remaining boxes: P, Q, T, V.

Determining Arrangement: Q, T, V, P

Using '3 boxes between Q and T' (4 positions apart) with remaining positions {2, 3, 5, 7}:

• Q and T must be at positions 7 and 3 (or 3 and 7).

Consider the constraints Q > V and V >= P + 2:

• If Q=7 and T=3: The partial arrangement is S _ T U _ R Q. Remaining {2, 5} for P, V.
• To satisfy Q(7) > V and V >= P + 2, V must be placed at 5 and P at 2. (Check: V=5, P=2 satisfies 5 >= 2 + 2).

This yields the complete arrangement (bottom to top):

Final Calculation

The question asks for the number of boxes between R and P.

• R is at Position 6.
• P is at Position 2.
• The boxes between them are at positions 3, 4, and 5 (T, U, V).

Therefore, there are 3 boxes between R and P.