- #1
zeb
- 33
- 0
Here's a problem that I need help figuring out...
imagine a 9x9 grid filled with the numbers 1-81 starting in the upper left corner and progressing left to right, top to bottom; like so:
Also imagine that within this grid of numbers are nine subdivisions which contain nine of the above numbers in a 3x3 grid (like a sudoku puzzle). Let's call these subdivisions blocks.
So the first block contains the numbers 1,2,3,10,11,12,19,20,21. The blocks are numbered 1-9 in the same direction (left to right, top to bottom) that the smaller squares are. So block #9 contains the numbers 61,62,63,70,71,72,79,80,81.
I need to come up with a formula to determine which block any given number is in. For example, the number 28 appears in block #4, number 20 appears in block #1, number 68 appears in block #8.
Any ideas?
imagine a 9x9 grid filled with the numbers 1-81 starting in the upper left corner and progressing left to right, top to bottom; like so:
Code:
/--------------------------------------------\
| 1, 2, 3 | 4, 5, 6 | 7, 8, 9 |
| 10, 11, 12 | 13, 14, 15 | 16, 17, 18 |
| 19, 20, 21 | 22, 23, 24 | 25, 26, 27 |
|--------------------------------------------|
| 28, 29, 30 | 31, 32, 33 | 34, 35, 36 |
| 37, 38, 39 | 40, 41, 42 | 43, 44, 45 |
| 46, 47, 48 | 49, 50, 51 | 52, 53, 54 |
|--------------------------------------------|
| 55, 56, 57 | 58, 59, 60 | 61, 62, 63 |
| 64, 65, 66 | 67, 68, 69 | 70, 71, 72 |
| 73, 74, 75 | 76, 77, 78 | 79, 80, 81 |
\--------------------------------------------/
Also imagine that within this grid of numbers are nine subdivisions which contain nine of the above numbers in a 3x3 grid (like a sudoku puzzle). Let's call these subdivisions blocks.
So the first block contains the numbers 1,2,3,10,11,12,19,20,21. The blocks are numbered 1-9 in the same direction (left to right, top to bottom) that the smaller squares are. So block #9 contains the numbers 61,62,63,70,71,72,79,80,81.
I need to come up with a formula to determine which block any given number is in. For example, the number 28 appears in block #4, number 20 appears in block #1, number 68 appears in block #8.
Any ideas?