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: Test option H1 as the southernmost hill.
From clues (i) and (ii), H2 and H3 must be the two middle hills, so H1 and H4 must be the two end hills, west and east, in some order. But clue (iii) says the southernmost hill cannot be the easternmost or the westernmost hill. Since H1 is always an end hill here, H1 can never be the southernmost hill, so this option is rejected right away.

Step 2: Test option H4 as the southernmost hill.
By the same reasoning as Step 1, H4 is also always one of the two end hills, H1 and H4 share the two end spots. So H4 also cannot be the southernmost hill by clue (iii), and this option is rejected too.

Step 3: Test option H2 as the southernmost hill.
Clue (iv) says exactly two hills sit to the west of H2, which places H2 in the 3rd spot from the west out of 4 positions. If H2 is the southernmost hill, clue (v) requires at least two hills to its east. But H2 is 3rd from the west, so only 1 hill, the 4th one, lies east of it. That is not at least two, so H2 fails clue (v) and is rejected.

Step 4: Test option H3 as the southernmost hill.
Since H2 sits in the 3rd spot and H1, H4 occupy the two end spots, H3 must sit in the only spot left, the 2nd spot from the west. If H3 is the southernmost hill, then two hills, the 3rd and 4th spots, lie to its east, meeting clue (v) exactly. H3 is also not an end hill, so it does not violate clue (iii). Every clue checks out for H3.

Final Answer:
Testing all four hills one by one against the five clues leaves only H3 standing, so H3 is the southernmost hill. \[ \boxed{\text{H3}} \]