The symbols O, *, $\Delta$ , and $\square$ are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows. Which symbol will occupy the box marked with '?' in the partially filled figure?
1) Every row and every column must contain each of the four symbols.
2) Every 2$\times$2 square delineated by bold lines must contain each of the four symbols. 
To solve the problem, we need to ensure that all rules of filling the symbols are followed:
- Every row and column must contain each of the four symbols: O, *, $\Delta$, and $\square$.
- Each 2x2 square must also contain each of the four symbols.
Let’s analyze the partially filled figure:
Our task is to determine which symbol will fill the position marked with ?.
- In the first row, symbols present are $\Delta$ and O. Therefore, the remaining symbols for this row are * and $\square$.
- In the first column, symbols present are O and *. Therefore, the remaining symbols for this column are $\Delta$ and $\square$.
- Within the top left 2x2 square:
- Current symbols are O, *.
- Missing symbols are $\Delta$ and $\square$.
Considering the missing symbols and given constraints, the only symbol that fulfills all conditions (one of which must be a *) for the box marked ? is *.
Therefore, the symbol that correctly occupies the box marked with ? is *.
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
