Question

Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:
i. Neither H2 nor H3 is the easternmost hill.
ii. Neither H2 nor H3 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 H2.
v. The southernmost hill has at least two hills to its east.
The southernmost hill is ________.

• A. H1
• B. H2
• C. H3
• D. H4

Hint:

First fix the west to east order using clues i, ii and iv, then use clues iii and v to pin down which hill is southernmost.

Answer 1

The Correct Option is C

Step 1: Use clues (i) and (ii) to place H2 and H3.
Clue (i) says H2 and H3 are not the easternmost hill. Clue (ii) says H2 and H3 are not the westernmost hill either. So neither H2 nor H3 sits at either end of the west to east line of hills. With 4 hills in a row, that leaves only the two middle positions for H2 and H3, and forces H1 and H4 to occupy the two end positions, though we do not yet know which of H1, H4 is on which end.

Step 2: Use clue (iv) to fix H2's exact position.
Clue (iv) says two hills lie to the west of H2. Counting positions from the west as 1st, 2nd, 3rd, 4th, having exactly two hills to the west of H2 means H2 itself is in the 3rd position. Since Step 1 already restricted H2 to one of the two middle positions, this confirms H2 is 3rd from the west, and therefore H3, the only other middle hill, takes the 2nd position.

Step 3: Write out the confirmed order.
From west to east, the order is now: position 1 (H1 or H4), position 2 = H3, position 3 = H2, position 4 (whichever of H1, H4 is left). The easternmost hill is position 4, and the westernmost hill is position 1.

Step 4: Use clue (iii) to shortlist the southernmost hill.
Clue (iii) says the southernmost hill is neither the easternmost hill nor the westernmost hill. From Step 3 those are position 1 and position 4, that is, H1 and H4 in some order. So the southernmost hill must be one of the two middle hills, H2 or H3.

Step 5: Use clue (v) to choose between H2 and H3.
Clue (v) says the southernmost hill has at least two hills to its east. If H2, position 3, were the southernmost hill, only position 4 lies to its east, just 1 hill, not enough. So H2 fails clue (v). If H3, position 2, is the southernmost hill, then positions 3 and 4 lie to its east, 2 hills, and that satisfies at least two.

Final Answer:
Only H3 satisfies every clue, so the southernmost hill is H3. \[ \boxed{\text{H3}} \]