Understanding the Ages of Seven Girls Puzzle

This question asks us to determine the relative ages of seven girls, G1, G2, G3, G4, G5, G6, and G7, based on a series of clues. We are told that no two girls have the same age, which means there is a unique ranking from oldest to youngest.

Analyzing the Clues for Age Ranking

Let's break down each clue given in the problem to build the age ranking from oldest (1st) to youngest (7th).

• Clue 1 & 2: Seven girls G1-G7, no two have the same age. This confirms a strict ranking of 7 positions.
• Clue 3: The age of G3 is less than only two girls. This means G3 is older than \(7 - 2 - 1 = 4\) girls. So, G3 is the 5th oldest girl.
  Ranking so far: _ > _ > _ > _ > G3 > _ > _
• Clue 5: The age of G6 is the lowest. This means G6 is the youngest girl, holding the 7th position.
  Ranking so far: _ > _ > _ > _ > G3 > _ > G6
• Clue 4: The age of G1 is greater than G4 and G7. This gives us the relationship G1 > G4 and G1 > G7.
• Clue 6: The age of G5 is not the highest and it is greater than G1. This gives us G5 > G1 and G5 is not 1st.

Deducing the Complete Age Ranking

We know the partial ranking is _ > _ > _ > _ > G3 (5th) > _ > G6 (7th). The girls G1, G2, G4, G5, G7 need to fit into the remaining positions (1st, 2nd, 3rd, 4th, 6th).

From clues 4 and 6, we have the combined relationship: G5 > G1 > G4 and G5 > G1 > G7. This shows a clear hierarchy among G5, G1, and {G4, G7}.

We know G5 is not the 1st position. Let's try placing G5 in the next available position.

• Can G5 be 2nd? If G5 is 2nd, then G1 must be in a position younger than 2nd but older than G4 and G7. The available spots younger than 2nd are 3rd, 4th, 6th.
• If G1 is 3rd, then G4 and G7 must be in positions younger than 3rd, but not 5th (G3) or 7th (G6). The available spots are 4th and 6th. This fits! So, G4 and G7 can occupy the 4th and 6th positions (the exact order between G4 and G7 is not determined yet, but it doesn't affect the overall ranking positions).
• If G5 is 2nd, and G1 is 3rd, and {G4, G7} are 4th and 6th, where does G2 fit? The only remaining position is 1st.

Let's check if this potential ranking fits all clues:

Proposed Ranking: G2 > G5 > G1 > {G4 or G7} > G3 > {G7 or G4} > G6

Positions:

Verifying clues against this ranking:

• G3 is 5th. She is less than G2, G5, G1, and the girl at 4th. She is older than the girl at 6th and G6. This fits "less than only two girls" (meaning older than exactly two girls). Yes.
• G1 (3rd) is greater than G4 and G7 (4th and 6th). Yes.
• G6 is the lowest (7th). Yes.
• G5 (2nd) is not the highest (not 1st) and is greater than G1 (3rd). Yes.

This ranking satisfies all the clues. Let's quickly consider if G5 could be in any other position (3rd, 4th, 6th) without being 1st. We already established that if G5 is 2nd, G1 must be 3rd for the structure G5 > G1 > {G4, G7} to fit into the available spots (1, 2, 3, 4, 6) alongside G2, G3 (5th), and G6 (7th). Any other placement of G5 or G1 lower down would require G4 and G7 to be in positions already occupied or lower than G6, which is impossible.

Answering the Question: Girls Older Than G5

The question asks: "The age of how many girls is greater than G5?"

Based on our deduced ranking:

G2 > G5 > G1 > {G4 or G7} > G3 > {G7 or G4} > G6

G5 is in the 2nd position. The girls older than G5 are those in positions higher than 2nd. Only the girl in the 1st position is older than G5.

The girl in the 1st position is G2.

Therefore, only one girl (G2) is older than G5.

The number of girls older than G5 is 1.

Revision Table: Age Ranking Analysis

Additional Information: Logic Puzzle Strategies

Logic puzzles like this require careful reading and systematic deduction. Here are some tips:

• Identify all individuals and attributes being compared (girls, ages).
• Note any constraints (no two same age).
• Translate each clue into a symbolic representation (e.g., G3 < only two girls becomes G3 is 5th).
• Build a visual aid like a ranking line or table.
• Combine clues to find chained relationships (e.g., G5 > G1 and G1 > G4, G7 leads to G5 > G1 > {G4, G7}).
• Place individuals with fixed positions first (G3 is 5th, G6 is 7th).
• Fit the chained relationships into the remaining spots, checking for contradictions.
• If multiple placements seem possible, test each one against all clues until only one valid ranking remains.
• Finally, answer the specific question asked based on the completed ranking.