Five chairs C01, C02, C03, C04 and C05 are placed one above the other but not necessarily in the same order. If C03 is above C02, C01 is above C05 but below C04 and C05 is above C03, which chair is in the middle?
C05
Understanding the Chair Arrangement Puzzle
This problem is a type of logic puzzle that requires us to deduce the correct order of five chairs (C01, C02, C03, C04, C05) based on a set of given clues about their relative positions, specifically which chair is placed above or below another. We are told the chairs are stacked one above the other. Our goal is to determine the exact sequence from top to bottom and identify the chair in the middle position.
Analyzing the Chair Positioning Clues
Let's break down the information provided in the puzzle:
- Clue 1: C03 is above C02. This tells us the relative position of C03 and C02.
- Clue 2: C01 is above C05 but below C04. This gives us a relationship between C01, C05, and C04.
- Clue 3: C05 is above C03. This provides another piece of information about the relative height of C05 and C03.
We need to combine these individual clues to build a complete picture of the chair stack.
Combining Clues to Determine Chair Order
Let's use the clues to establish longer chains of relationships. If chair A is above chair B, we can represent this as A > B.
- From Clue 1: C03 > C02
- From Clue 3: C05 > C03
Combining these two, we see a sequence: C05 is above C03, and C03 is above C02. This means the partial order is C05 > C03 > C02. So, C05 is at the highest position among these three, followed by C03, then C02 at the lowest.
Now let's look at Clue 2:
- From Clue 2: C01 is above C05, and C01 is below C04. This gives us the relationship C04 > C01 > C05. This means C04 is above C01, and C01 is above C05.
We now have two important sequences:
- C05 > C03 > C02
- C04 > C01 > C05
Notice that C05 appears in both sequences. Sequence (2) tells us that C04 is above C01, which is above C05. Sequence (1) tells us that C05 is above C03, which is above C02. By connecting these at C05, we can form a complete order for all five chairs:
C04 is above C01, and C01 is above C05. Since C05 is above C03 and C02, the complete order from top to bottom is:
C04 > C01 > C05 > C03 > C02
Identifying the Middle Chair Position
The five chairs are arranged in a stack. In a stack of five items, the middle item is the third one from either the top or the bottom. Based on our determined order from top to bottom (C04, C01, C05, C03, C02), we can list the positions:
| Position (from Top) | Chair |
|---|---|
| 1st | C04 |
| 2nd | C01 |
| 3rd (Middle) | C05 |
| 4th | C03 |
| 5th | C02 |
Looking at the table, the chair in the 3rd position, which is the middle position in a stack of five, is C05.
Chair Arrangement Puzzle Solution Summary
By carefully combining the given clues about the relative positions of the five chairs C01, C02, C03, C04, and C05, we established the complete order of the chairs from top to bottom. This order is C04, C01, C05, C03, and C02. In a stack of five items, the item in the third position is the middle one. Therefore, the chair located in the middle is C05.
Revision Table: Chair Arrangement Puzzle
| Clue | Relationship |
|---|---|
| C03 is above C02 | C03 > C02 |
| C01 is above C05 but below C04 | C04 > C01 > C05 |
| C05 is above C03 | C05 > C03 |
| Combined Relationships | C04 > C01 > C05 > C03 > C02 |
Additional Information: Logic Puzzles and Ordering
Logic puzzles like this chair arrangement problem test your ability to use deductive reasoning. You are given a set of facts or clues, and you must combine them logically to reach a conclusion. Ordering puzzles involve arranging items based on their relative positions (like height, time, or spatial location).
Key strategies for solving ordering puzzles:
- Identify all the items involved.
- List each clue separately.
- Translate clues into symbolic notation (like A > B) if helpful.
- Look for common items in different clues to link them together.
- Build a longer chain or sequence by connecting the individual relationships.
- Once the full order is established, identify the position requested (e.g., middle, top, bottom).
Practicing different types of ordering and sequencing puzzles can help improve your logical thinking and problem-solving skills.
Important Questions from Linear Arrangement
Seven people, A, B, C, D, E, F and G, are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
P, Q, R and S are sitting on a bench and facing in the same direction. P sits next to Q but not next to R. S, who is sitting on the extreme right, does not sit next to either Q or R. How many of them each have two neighbors?
Five friends Ram, Priya, Raunak, Aditya and Shyam are sitting in a row facing north. Raunak is to the right of Shyam and Priya is to the left of Shyam but to the right of Rama. Raunak is to the left of Aditya. Who is fourth from the left end?
Six people P, Q, R, S, T and U sit in a row, not necessarily in the same order. If two persons sit in between P and Q, and two persons sit in between T and U, then how many persons sit in between R and S?
Six persons P, Q, R, S, T and U are sitting in a row facing north (not necessarily in the same order). Q sits fourth to the right of S. One person sits between P and Q. Three persons sit between R and T. R sits immediate left of P. How many persons sit between T and U?
