About Puzzle Test
A puzzle test question describes people on different floors of a building, boxes in a stack, or something similar, and gives clues about who is above whom. The clues identify one arrangement, and because the positions are numbered the top and bottom are fixed points to build the rest of the puzzle around.
What you need to understand
- Floor 1 is the lowest and the highest floor number is the top, so above always means a larger number.
- Immediately above means the next floor up; somewhere above only says higher than.
- Second above B means two floors higher, which leaves exactly one floor between them.
- The top and bottom are the only positions a single clue can fix outright, so they are worth placing first.
- A chain of clues such as A above B, B above C is stronger than the same clues taken separately.
- If the clues are consistent, exactly one arrangement fits them all.
How to work through these questions
- Draw the floors as a vertical column before re-reading the clues.
- Fill in the top and bottom floors and anyone named with an exact floor.
- Work through the immediate clues, which place two people relative to each other.
- Leave the somewhere above or below clues until last, when they can only eliminate what remains.
- Read the clues back against the finished column to check none is contradicted.
- Answer only what is asked: which floor, who is on it, or how many lie between two people.
Mistakes that cost marks
- Counting the number of floors apart when the question asks how many people are between.
- Treating above as a smaller floor number and building the column upside down.
- Reading immediately above as though it were somewhere above, and losing a constraint.
- Using a somewhere above clue too early, before the stronger clues have been used.
- Forgetting that the top floor carries the highest number, not floor 1.
- Answering from an arrangement that satisfies most of the clues but not all of them.
Worked example
Six people P, Q, R, S, T and U live on six different floors, with floor 1 the lowest and floor 6 the highest. Q lives on floor 2. T lives immediately above Q. P lives on the top floor. S lives immediately below P. R lives above U. Who lives on floor 4?
- Q lives on floor 2.
- T lives immediately above Q, so T is on floor 3.
- P lives on the top floor, which is floor 6.
- S lives immediately below P, so S is on floor 5.
- Floors 1 and 4 are still free, for R and U. R lives above U, so U takes floor 1 and R takes floor 4.
Answer: R
Practice questions with answers
A few Puzzle Test questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
Six people P, Q, R, S, T and U live on six different floors of a building. Floor 1 is the lowest and floor 6 is the highest. (1) exactly 1 person lives between P and T. (2) U lives second below Q. (3) S lives third above R. (4) R lives second below P. Who lives on floor 5?
Answer: Option D — with explanation
Only one assignment of the 6 people to floors satisfies all 4 clues, and in it S occupies floor 5.
Common mistakes
- read a clue as naming the immediate neighbour when it named someone further off: U
- placed two people the other way round and shifted the rest along: R
- took left to mean right: P
Question 2
Six people P, Q, R, S, T and U live on six different floors of a building. Floor 1 is the lowest and floor 6 is the highest. (1) U lives somewhere below R. (2) T lives third below Q. (3) Q lives immediately below U. (4) T lives immediately below S. How many people live between R and T?
Answer: Option C — with explanation
Only one assignment of the 6 people to floors satisfies all 4 clues. In it R and T have 4 floors between them.
Common mistakes
- counted one of the two end people as though they were between them: 5
- left out one of the people in the middle: 3
- left out two of the people in the middle: 2
Question 3
Seven people P, Q, R, S, T, U and V live on seven different floors of a building. Floor 1 is the lowest and floor 7 is the highest. (1) S lives third below U. (2) V lives second above R. (3) Q lives sixth above R. (4) T lives second below P. Who lives on the top floor?
Answer: Option B — with explanation
Only one assignment of the 7 people to floors satisfies all 4 clues, and in it Q occupies floor 7, the top floor.
Common mistakes
- counted the positions from the wrong end: V
- took left to mean right: T
- placed two people the other way round and shifted the rest along: R
Question 4
Five people P, Q, R, S and T live on five different floors of a building. Floor 1 is the lowest and floor 5 is the highest. (1) R lives immediately below S. (2) R lives between P and Q. (3) P lives fourth above T. Who lives on floor 1?
Answer: Option A — with explanation
Only one assignment of the 5 people to floors satisfies all 3 clues, and in it T occupies floor 1.
Common mistakes
- counted the positions from the wrong end: Q
- placed two people the other way round and shifted the rest along: R
- read a clue as naming the immediate neighbour when it named someone further off: P
Question 5
Five people P, Q, R, S and T live on five different floors of a building. Floor 1 is the lowest and floor 5 is the highest. (1) R lives between Q and P. (2) Q lives third below T. (3) S lives second below P. Who lives on the lowest floor?
Answer: Option D — with explanation
Only one assignment of the 5 people to floors satisfies all 3 clues, and in it Q occupies floor 1, the lowest floor.
Common mistakes
- counted the positions from the wrong end: T
- took left to mean right: P
- read a clue as naming the immediate neighbour when it named someone further off: S
Frequently asked questions
Should floor 1 be drawn at the top or the bottom?
At the bottom. Floor 1 is the lowest floor, so drawing it at the bottom makes above point up the page and matches the wording of the clues.
How many floors lie between two people two floors apart?
One. Being two floors apart means exactly one floor lies between them, so those two counts are not the same number.
What is the difference between immediately above and somewhere above?
Immediately above means the very next floor with nothing in between. Somewhere above only says the person lives higher up, which places them far less precisely.
Which clues are worth using first?
Those that fix a person completely: an exact floor, the top floor, the bottom floor, or an immediate relationship with someone already placed.
What if two arrangements seem to fit the clues?
A clue has been misread. Check the direction of every above and below, since reversing one of them usually produces the second arrangement.
