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 ________.
Hill Arrangement Logic Puzzle
We need to determine the positions of four hills (H1, H2, H3, H4) based on the given clues and identify the southernmost hill.
East-West Positioning
Let's denote the positions from West to East as 1, 2, 3, 4.
- Clues (i) and (ii) state that neither H2 nor H3 is the easternmost (position 4) or westernmost (position 1). So, H2 and H3 can only be in positions 2 or 3.
- Clue (iv) states that two hills are to the west of H2. This means H2 cannot be in position 1 or 2. H2 must be at least in position 3.
- Combining these deductions: H2 cannot be 1, 2, or 4. Therefore, H2 must be in position 3. The order is: _ , _ , H2 , _ (West to East).
- Since H3 cannot be 1 or 4 (clues i, ii) and cannot be 3 (H2 is there), H3 must be in position 2. The order is: _ , H3 , H2 , _ (West to East).
- This leaves H1 and H4 for positions 1 and 4. The arrangement is [H1/H4] , H3 , H2 , [H1/H4].
North-South Positioning
Now let's determine the southernmost hill using North-South clues.
- Clue (iii) states that the easternmost (position 4) and westernmost (position 1) hills are not the southernmost.
- Clue (v) states that the southernmost hill has at least two hills to its east.
- If the southernmost hill was H2 (position 3), it would only have one hill (position 4) to its east. This violates clue (v).
- If the southernmost hill was the hill at position 4 (easternmost), it would have zero hills to its east. This violates clue (v).
- Therefore, the southernmost hill must be either the hill at position 1 or position 2 (West to East).
- From clue (iii), the hill at position 1 is not southernmost.
- This leaves only the hill at position 2 as the potential southernmost hill.
- The hill at position 2 is H3.
Conclusion
Based on the deductions:
- The East-West order is [H1/H4], H3, H2, [H1/H4].
- The southernmost hill cannot be the westernmost (position 1) or easternmost (position 4) hill (Clue iii).
- The southernmost hill cannot be H2 (position 3) as it doesn't have two hills to its east (Clue v).
- The only remaining hill that satisfies all conditions, including having at least two hills to its east (H2 and the hill at pos 4), is H3 (position 2).
Therefore, H3 is the southernmost hill.
Important Questions from Puzzles
The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?
Note: The figure shown is representative.
- A thin wire is used to construct all the edges of a cube of $1 \text{ m}$ side by bending, cutting and soldering the wire. If the wire is $12 \text{ m}$ long, what is the minimum number of cuts required to construct the wire frame to form the cube?
In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.
1 1 2 2 X 3 2 X 4 1 2 X Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals).
As per this rule, the maximum number of crosses possible in the empty column is
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is
In the 4 x 4 array shown below, each cell of the first three rows has either a cross (X) or a number.
1 X 4 3 X 5 5 4 3 X 6 X
The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is
