Solving the Height Comparison Puzzle

This question asks us to determine the shortest person among a group based on several height comparisons. We need to carefully analyze each statement and combine them to establish a relative height ranking.

Analyzing the Statements

Let's represent the height comparisons using inequality symbols:

• A is taller than B: \(A > B\)
• C and D are of equal height: \(C = D\)
• E is shorter than B but taller than D: \(B > E\) and \(E > D\). Combining these, we get \(B > E > D\).
• F is shorter than C, who is shorter than B: \(F < C\) and \(C < B\). Combining these, we get \(B > C > F\).

Combining the Comparisons

Now, let's put these inequalities together:

1. From the statements, we have \(A > B\). A is taller than B.
2. We have \(B > E > D\). E is between B and D in height.
3. We have \(B > C > F\). C is between B and F in height, and B is taller than C, C is taller than F.
4. We also know \(C = D\).

Let's substitute \(C\) for \(D\) in the inequality \(B > E > D\). Since \(C = D\), we get \(B > E > C\).

Now we have:

• \(A > B\)
• \(B > E > C\)
• \(B > C > F\)
• \(C = D\)

From \(B > E > C\) and \(B > C > F\), B is the tallest among E, C, and F. We need to compare E, C, D, and F to find the shortest.

We know \(E > C\) (from \(B > E > C\)).

We know \(C > F\) (from \(B > C > F\)).

Since \(C = D\) and \(C > F\), it implies \(D > F\).

So, we have established the relationships:

• \(E > C\)
• \(C > F\)
• \(D > F\) (because \(C=D\) and \(C > F\))

Combining these, we get \(E > C > F\). Also, since \(C=D\), we have \(E > C = D > F\).

Let's consolidate the ranking from tallest to shortest based on our findings:

1. A is taller than B (\(A > B\)).
2. B is taller than E and C (\(B > E\) and \(B > C\)).
3. E is taller than C (\(E > C\)).
4. C and D are equal in height (\(C = D\)).
5. C is taller than F (\(C > F\)).
6. Since \(C=D\) and \(C > F\), D is also taller than F (\(D > F\)).
7. From \(E > C\) and \(C > F\), it follows that \(E > F\).

Putting it all together, we can establish a possible height order from tallest to shortest:

\(A > B > E > C = D > F\)

This ranking shows that F is the shortest among all the individuals A, B, C, D, E, and F.

Summary of Heights

Based on the derived ranking \(A > B > E > C = D > F\), the shortest person is F.

Revision Table: Height Comparison

Additional Information: Logic and Reasoning Puzzles

Height comparison problems are a common type of logical reasoning puzzle. They test your ability to interpret relational statements and combine them to form a complete picture or ranking. Here are some tips for solving such puzzles:

• Use symbols (\(>\), \(<\), \(=\)) to represent the relationships clearly.
• Write down each piece of information as a separate inequality or equality.
• Look for common elements in the statements to link the inequalities together.
• Combine overlapping relationships to create longer chains of inequalities (e.g., if A > B and B > C, then A > C).
• Substitute equals (e.g., if C = D, replace C with D or D with C in other statements).
• Once a complete or partial ranking is established, answer the specific question asked (tallest, shortest, middle, etc.).
• Drawing a simple diagram or list can also help visualize the relative positions.

These puzzles help improve analytical thinking and deductive reasoning skills, which are valuable in many areas.