Seven boxes P, Q, R, S, T, U, and V are placed one above the other in a stack. Only two boxes are placed between box S and box V. Only one box is placed between box Q and box T. Bo... Seven boxes P, Q, R, S, T, U, and V are placed one above the other in a stack. Only two boxes are placed between box S and box V. Only one box is placed between box Q and box T. Box T is placed immediately below box R. Box T is placed between box U and box Q. Only one box is placed between box R and box P. Box P is placed just above box V. Read more

Steps to Solve

1. Establish P and V's positions Box P is just above box V. We can represent this as P immediately above V (P/V).

2. Incorporate S's position Only two boxes are placed between box S and box V. This gives us two possibilities: S _ _ V or V _ _ S Combining this with step 1 we have : S _ _ P/V or P/V _ _ S

3. Incorporate R and T's positions Box T is placed immediately below box R. This gives us R/T. Box T is placed between box U and box Q. So U/T/Q or Q/T/U.

4. Combining R, T, U, and Q

   Since T is immediately below R, we can combine (R/T) with either (U/T/Q) or (Q/T/U), yielding two possible sequences: R/T/U/Q or Q/U/T/R. However, from the prompt, only one box is between Q and T, therefore Q/T for the former and T/Q for the latter. We know that R/T, we get that Q/T, as T is between Q and U implies that Q and U are on either side of T thus boxes U, T, and Q must be in the order Q/T/U or U/T/Q . T is immediately below R and T BETWEEN Q and U, implies R/T is a block. This block CANNOT be above Q or U. Therefore boxes U, T, and Q must be in the order Q/T/U or R/T/U, and the third case being U/Q/T (not possible). Therefore, the only sequence possible is Q/U/T cannot happen either. U/T/Q. Therefore, the boxes must be arranged as R/T with T in between U and Q makes, it possible for arrangement such as U/T/Q or Q/T/U only, box T must be immediate below R so it becomes R/T where by definition, there exist cases R _ Q/T/U or cases where R/T is below Q/T/U

5. Incorporate R and P's positions Only one box is placed between box R and box P. We denote this as R _ P or P _ R. Since P is directly above V, this becomes R _ P/V or P/V _ R

6. Synthesize all constraints We have:

   • P/V
   • S _ _ P/V OR P/V _ _ S
   • R/T
   • Box T is placed between box U and box Q which can only mean U/T/Q or Q/T/U
   • R _ P/V or P/V _ R

7. Deduce the order

   Let us explore P/V _ _ S and R _ P/V and U/T/Q and R/T It means R _ P/V _ _ S or U/T/Q

   Given the constratints R/T and R _ P/V: we have R/T/ _ / P/V since R _ P/V It means R/T/U/P/V However, we are given box R and box P. Box P is placed just above box V. we are told only 1 box between R and P we deduce So either R _ P/V or P/V _ R but P/V _ R is incorrect, therefore we have R/T ONLY 2 BOXES between S and V ONLY 1 box between Q and T implies Q/T or T/Q T is immediately below R -> R/T T is between U and Q -> U/T/Q OR Q/T/U ONLY 1 box between R and P P is just above V implies P/V

   Therefore, from constraints U/T/Q -> R must be above U and P must be below Q. This means that we will have S - 1 U - 2 R - 3 T -4 Q -5 P - 6 V - 7 This fits our rules: T is between Q and U. Therefore, our answer is S/U/R/T/Q/P/V