8 Children with Comic Books Floor Stay Reasoning Puzzle

8 children live in eight floors: ground floor 1 to top floor 8. They have different numbers of comic books. Solve the reasoning puzzle from 15 clues.

The 8 Children Floor Stay Reasoning Puzzle

Description

In an eight-storied building, having floors numbered 1 to 8 from bottom to top, eight children A, B, C, D, E, F, G and H each live on a different floor not necessarily in the order of floor numbers. The children have different number of comic books with them 11, 16, 19, 25, 34, 41, 46 and 50, also not necessarily in the same order as their names or floors.

Clues:

1. The child who lives on 6th floor has 25 comic books.
2. One child lives between F and the one having 25 comic books.
3. G lives below F on an even numbered floor.
4. G does not have 25 comic books.
5. Child having 46 comic books lives just above G.
6. Two children Live between F and H.
7. H lives below F.
8. Total of number of comic books with D and H is a multiple of 4.
9. Two children live between A and the child having 41 comic books.
10. A lives above G.
11. The one having 41 comic books lives above A.
12. B has 34 comic books.
13. The one having 11 comic books lives just above the one having 16 comic books.
14. 1 child lives between C and E.
15. The difference between the number of comic books with E and G is 6.

Questions

Question 1. Which of the following is correct?

1. Two children live between D and the child having 11 comic books.
2. G lives on the floor just below F.
3. A has minimum number of comic books.
4. E has 19 comic books.
5. None of these.

Question 2. On which of the following floors does D live?

1. floor 1.
2. floor 3.
3. floor 5.
4. floor 4.
5. None of these.

Question 3. Child having 50 comic books lives on,

1. floor 7.
2. floor 4.
3. floor 2.
4. floor 1.
5. None of these.

Question 4. Who lives just above A and with how many comic books?

1. E with 25 comic books.
2. C with 46 comic books.
3. D with 19 comic books.
4. B with 34 comic books.
5. None of these.

Question 5. Who lives two floors above B?

1. F.
2. E.
3. C.
4. D.
5. None of these.

Time to solve is 30 minutes. For experienced puzzle solvers, the time should be comfortable enough.

Hints:

• Use strategies of direct assignment first, techniques based on link references in a Clue for already assigned property values and two-valued assignments.
• Scan the Clues to identify the promising position relationship of two property values.
• Use these horizontal bonds appropriately.
• Identify hidden patterns in the number of comic books owned by the children.

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Solution to The 8 Children Floor Stay Reasoning Puzzle: Preparation

Understanding the objects and their roles

Primary object which forms the header:

• Floor 1 to 8 is the primary object used as the header against each of which the values of the properties will be noted when assigned.

"Assigned" means placing the value in its correct position.

Secondary objects as properties which represent the rows:

• Children: A, B, C, D, E, F, G, H—forms the first row.
• Comic book #: 11, 16, 19, 25, 34, 41, 46, 50—forms the second row.

Showing assignments for the property values

• Conventional approach: Vertical Floors as in real life—1 to 8 from bottom to top.
• Convenient approach: Horizontal Floors 1 to 8 from left to right with directions Down towards left and Up towards right shown with the assignment table.
• Why this arrangement: In most of the reasoning puzzles, horizontal header row and property row are used. This forms a norm that makes analysis of clues and assignments more convenient.

The assignment table at the start:

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Solution to The 8 Children Floor Stay Reasoning Puzzle: Clue analysis for solution

Stage 1: Assignments directly and by pattern identification, two-valued probables and two-position-block

Clue 1. "The child who lives on 6th floor has 25 comic books."

• Result: Comic books # 25 for floor 6.

Clue 4. "G does not have 25 comic books."

• Result: "not G" for floor 6.

Clue 15. "The difference between the number of comic books with E and G is 6."

• Breakthrough result: Only 19 and 25 have a difference of 6: E in floor 6 with 25 comic books and G in yet unknown floor has 19 comic books (remember to use when time comes).

Clue 14. "1 child lives between C and E."

• Result: C lives either in floor 4 or floor 8 with second probable occupant unknown at this moment. This is a two-valued assignment with certainty increased from 1 out of 8 to 1 out of 2.

Clue 2. "One child lives between F and the one having 25 comic books."

• Results:
• F also lives either in floor 4 or floor 8 with second occupant as C.
• F and C can only occupy these two floors and no other child.
• This is a Two-Position Block—an advanced pattern valuable for getting breakthroughs.
• Effectively, these two floors are occupied (though out of the two occupants F and C, it is not known yet who will occupy which of the two floors 4 and 8).

Clue 3. "G lives below F on an even numbered floor."

• Breakthrough result: As F and C have blocked the even numbered floors 4 and 8, with E occupying the third even numbered Floor 6, G must occupy floor 2, the only even numbered floor still not occupied.
• Additional assignment: G has 19 comic books (by Clue 15).

Clue 5. "Child having 46 comic books lives just above G."

• Result: Comic book number for the child in floor 3 is 46.

A group of two Clues analyzed together:

Clue 6. "Two children Live between F and H."

Clue 7. "H lives below F."

• Result of Clues 6 and 7 combined: By the Horizontal Bond H-floor-floor-F, H lives either in floor 1 (when F is in floor 4) or in floor 5 (when F is in floor 8)

The stage 1 assignment table:

Stage 2: Critical breakthrough by the second four-position Horizontal Bond

A group of two clues analyzed together:

Clue 9. "Two children live between A and the one having 41 comic books."

Clue 11. "The one having 41 comic books live above A."

• Result of Clues 9 and 11: The upward-downward four-position horizontal bond between A and 41 reduces to "A-floor-floor-41" with two probables: A in floor 1 or floor 5 (A cannot be in floor 3 as three floor up, the child in floor 6 already has 25 comic books).

Clue 10. "A lives above G."

• Breakthrough results: A cannot be in floor 1 below G.
• A must be in floor 5.
• Assignments: A in floor 5, Comic book # 41 in floor 8, H in floor 1.
• Additional assignments: With H in floor 1, F in floor 4 and C in floor 8 (by Clue 6: Two children Live between F and H).

Stage 2 assignments shown.

Stage 3: No more hurdles—Straightforward assignments to the solution

Clue 12. "B has 34 comic books."

• Result: B and 34 are in floor 7 (this is the only position free for the vertical bond "B-34").
• Additional assignment: D in floor 3 as it is the only floor free.

Clue 8. "Total of number of comic books with D and H is a multiple of 4."

• Result: H in floor 1 has 50 books (as sum of 50 and 46 is 96, a multiple of 4, and the only one such probable between the remaining numbers 50, 11, and 16 to be added to 46 for D).

Clue 13. "The one having 11 comic books lives just above the one having 16 comic books."

• Result: 16 in 4 and 11 in 5 (the only free two positions for the horizontal bond "16-11").

The completed assignments:

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Answers to the questions

Question 1. Which of the following is correct?

1. Two children live between D and the child having 11 comic books.
2. G lives on the floor just below F.
3. A has minimum number of comic books.
4. E has 19 comic books.
5. None of these.

Answer 1. Option 3: A has minimum number of comic books.

Question 2. On which of the following floors does D live?

1. floor 1.
2. floor 3.
3. floor 5.
4. floor 4.
5. None of these.

Answer 2. Option 2: floor 3.

Question 3. Child having 50 comic books lives on,

1. floor 7.

2. floor 4.

3. floor 2.

4. floor 1.

5. None of these.

Answer 3. Option 4: floor 1.

Question 4. Who lives just above A and with how many comic books?

1. E with 25 comic books.
2. C with 46 comic books.
3. D with 19 comic books.
4. B with 34 comic books.
5. None of these.

Answer 4. Option 1: E with 25 comic books.

Question 5. Who lives two floors above B?

1. F.
2. E.
3. C.
4. D.
5. None of these.

Answer 5. Option 5: None of these (as B is in floor 7, two floors above B there is no floor in this eight floor building).

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Comments

With the experience gained till now in solving reasoning puzzles, this hard floor stay reasoning puzzle could have been solved at one go. But, for you to know what happened in between, the solution is split into three stages.

Highlights of the puzzle solution:

1. Get assignments as soon as possible: In the first stage itself, along with direct assignments, Clues with horizontal bonds and conflicts were exploited to get significant number of assignments.
2. Use of loose implication as soon as possible: The unused hanging implication of G having 19 comic books obtained by Clue 15 (it could not be used then, as position of G was not known at that point of time), is ultimately used when position of G is identified by Clue 3. This is an important activity for quick and flawless solution. In the same way, implications of Clue 6 are fully used to resolve the positions of F and C when position of H is obtained by Clue 10.
3. Use of advanced positional relations: The horizontal bonds, fixed two-position bonds and two-valued two-position block are fully exploited.

This relatively hard reasoning puzzle is from a Bank PO recruitment test for selecting bright and sharp minds.

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