Sanjay loves playing with patterns. He marks five dates in a calendar that form the shape of a plus sign (\(+\)). The shape consists of a central date(represented as \(n\)), the date directly above it, the date directly below it, the date to its left, and the date to its right.
| Sun | Mon | Tue | Wed | Thu | Fri | Sat |
| \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) |
| \(8\) | \(9\) | \(10\) | \(11\) | \(12\) | \(13\) | \(14\) |
| \(15\) | \(16\) | \(17\) | \(18\) | \(19\) | \(20\) | \(21\) |
1. Sanjay finds that the sum of all five dates in his plus sign is 60. The value of the central date(\(n\)) is
2. What will be the new sum of \(5\) dates if he changes the shape from a plus sign (\(+\)) to an "X" shape using the four immediate diagonal neighbors around the center date \(11\).
3. Consider any \(3 \times 3\) calendar grid. Let \(S_{1}\) be the sum of the top-left and bottom-right numbers. Let \(S_{2}\) be the sum of the top-right and bottom-left numbers. Which statement is true?
4. In a leap year, January \(1^{st}\) falls on a Tuesday. On what day of the week will February \(1^{st}\) of that same year fall?