A, B, C, D, E, and F, each have different heights. Only

Solution

F can be 164 cm, 166 cm, or 168 cm .

Reasoning (concise):

• Six people have distinct heights; shortest = 160 , tallest = 174 .

• D = 162 , A = 170 .

• “Only one person is taller than C” ⇒ C is second tallest , so the tallest (174) is someone else.

• B is not 160 , and F is shorter than A (170) but taller than D (162) ⇒ F must be one of 164, 166, 168.

• 160 cannot be B (B ≠ 160) and cannot be A, D, or F (given values/constraints), so 160 must be E; 174 must be B; C becomes the remaining highest value (e.g., 172).

• All three candidates 164, 166, 168 for F are consistent with the conditions.