Q1.
Can we find the 4 numbers in the grid from just knowing this sum?
Answer
Yes — the sum decides all four numbers. Let a be the top-left date of the 2 × 2 square.
| a | a + 1 |
|---|---|
| a + 7 | a + 8 |
Sum = a + (a + 1) + (a + 7) + (a + 8) = 4a + 16
So a = (Sum – 16) ÷ 4
So a = (Sum – 16) ÷ 4
The example on the page checks out: for 6, 7, 13, 14 the sum is 40, and (40 – 16) ÷ 4 = 6 — the top-left date.
Why it happens: a calendar row is a week, so the box directly below any date holds a date 7 larger; the box to the right holds one more. That fixed spacing is what lets all four numbers be written in terms of the single letter-number a. Once the four cells are 4 copies of a plus the fixed extra 0 + 1 + 7 + 8 = 16, the sum determines a, and a determines the rest.
Tip: not every number can be such a sum. Since Sum = 4a + 16, the sum must be a multiple of 4 — and a must sit in a place where the 2 × 2 square actually fits inside the month.