Q1.
Create your own calendar trick. For instance, choose a grid of a different size and shape.
Answer
Any shape works — you only have to write every cell in terms of one letter-number. Here are three tricks, all on the August 2025 page.
1. The 3 × 3 square. Let c be the middle date. The nine dates are:
| c – 8 | c – 7 | c – 6 |
| c – 1 | c | c + 1 |
| c + 6 | c + 7 | c + 8 |
Sum = 9c + (–8 – 7 – 6 – 1 + 0 + 1 + 6 + 7 + 8) = 9c
So: “Tell me the sum, and I divide by 9 to get the middle date.”
So: “Tell me the sum, and I divide by 9 to get the middle date.”
Try it on 11, 12, 13 / 18, 19, 20 / 25, 26, 27: the sum is 171, and 171 ÷ 9 = 19, the middle date. ✓
2. The plus-shape (5 cells). With c in the centre the cells are c – 7, c – 1, c, c + 1, c + 7, so the sum is 5c — divide by 5.
3. A 2 × 3 rectangle. With a at the top-left the cells are a, a + 1, a + 2, a + 7, a + 8, a + 9, so the sum is 6a + 27 — subtract 27 and divide by 6.
Why it happens: a calendar is a grid with a fixed step of 1 across and 7 down, so every cell of a chosen shape is c plus a fixed number. Adding them gives (number of cells) × c + (a fixed total). If your shape is symmetric about its centre, those fixed numbers cancel in pairs and the constant is 0 — which is why the 3 × 3 and the plus-shape give such clean tricks.
Try This: the second grid printed on this page is not a calendar — it runs 2 to 50 with ten numbers in a row. There the step downwards is 10, not 7, so a 2 × 2 square gives a + (a + 1) + (a + 10) + (a + 11) = 4a + 22. Every trick has to be re-derived for the grid it lives on.