Four hills $H_1, H_2, H_3$, and $H_4$ are present in an area. The following observations are made about them:
(i) Neither $H_2$ nor $H_3$ is the easternmost hill.
(ii) Neither $H_2$ nor $H_3$ is the westernmost hill.
(iii) Neither the easternmost hill nor the westernmost hill is the southernmost hill.
(iv) Two hills are located to the west of $H_2$.
(v) The southernmost hill has at least two hills to its east.
The southernmost hill is .

Question

Pointing to a photograph, a man says, "I have no brothers or sisters, but the father of the person in the photograph is my father’s son." Who is the person in the photograph?

Answer 1

This question is a placement puzzle. Instead of algebra, list the four positions from west to east as 1, 2, 3, 4 and place the hills by elimination, one clue at a time.

Clues (i) and (ii) together: $H_2$ and $H_3$ cannot be at position 1 (west end) or position 4 (east end), so they must both sit somewhere in the middle, at positions 2 and 3 in some order. That forces $H_1$ and $H_4$ to take the two end positions, 1 and 4, in some order.
Clue (iv): two hills sit west of $H_2$. Of the two middle slots (2 and 3), only position 3 has two positions (1 and 2) to its west. So $H_2$ is at position 3, and $H_3$ takes the only slot left in the middle, position 2.
Clue (iii): the southernmost hill is not at position 1 or position 4. Since $H_1$ and $H_4$ occupy positions 1 and 4, neither of them can be the southernmost hill. That leaves $H_2$ (position 3) or $H_3$ (position 2) as candidates.
Clue (v): the southernmost hill needs at least two hills to its east. $H_2$ sits at position 3, so only 1 hill (position 4) is east of it, too few. $H_3$ sits at position 2, so 2 hills (positions 3 and 4) are east of it, which is enough.

Only $H_3$ survives every clue, so $H_3$ is the southernmost hill.

Let's summarize:

$H_1$ and $H_4$ are stuck at the two ends (east and west), so clue (iii) rules them both out.
$H_2$ sits third from the west, leaving only one hill to its east, which clue (v) rejects.
$H_3$ sits second from the west, with two hills to its east, matching every clue.

The correct answer is $H_3$, option (C).

Answer 2

This question is a placement puzzle. Instead of algebra, list the four positions from west to east as 1, 2, 3, 4 and place the hills by elimination, one clue at a time.

Clues (i) and (ii) together: $H_2$ and $H_3$ cannot be at position 1 (west end) or position 4 (east end), so they must both sit somewhere in the middle, at positions 2 and 3 in some order. That forces $H_1$ and $H_4$ to take the two end positions, 1 and 4, in some order.
Clue (iv): two hills sit west of $H_2$. Of the two middle slots (2 and 3), only position 3 has two positions (1 and 2) to its west. So $H_2$ is at position 3, and $H_3$ takes the only slot left in the middle, position 2.
Clue (iii): the southernmost hill is not at position 1 or position 4. Since $H_1$ and $H_4$ occupy positions 1 and 4, neither of them can be the southernmost hill. That leaves $H_2$ (position 3) or $H_3$ (position 2) as candidates.
Clue (v): the southernmost hill needs at least two hills to its east. $H_2$ sits at position 3, so only 1 hill (position 4) is east of it, too few. $H_3$ sits at position 2, so 2 hills (positions 3 and 4) are east of it, which is enough.

Only $H_3$ survives every clue, so $H_3$ is the southernmost hill.

Let's summarize:

$H_1$ and $H_4$ are stuck at the two ends (east and west), so clue (iii) rules them both out.
$H_2$ sits third from the west, leaving only one hill to its east, which clue (v) rejects.
$H_3$ sits second from the west, with two hills to its east, matching every clue.

The correct answer is $H_3$, option (C).

Show Hint

The Correct Option is C

Solution and Explanation

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