Forty-two pieces, numbered from 1 to 42, are disposed in a 6x7 grid, so that each pair of consecutive numbers are in cells that touch each other horizontally or vertically, not diagonally. Below, there are two partial drawings of the grid, where only 3 numbers appear, but only one of the two is correct.
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
| | 11 | 20 | | | | | | | 11 | 20 | | | | |
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
| | | | | | | | | | | | | | | |
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
| | | | | | | | | | | | | | | |
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
| | | | | | | | | | 31 | | | | | |
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
| | 31 | | | | | | | | | | | | | |
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
| | | | | | | | | | | | | | | |
+----+----+----+----+----+----+----+ +----+----+----+----+----+----+----+
(first drawing) (second drawing)Justify what is the correct drawing and complete its filling.
Imagine the 6x7 grid is covered by a checkerboard pattern. Consecutive numbers alternate between even and odd, and so all even numbers will end up on the same color square. The second drawing violates this requirement, so it is incorrect.
The first drawing is correct:
+----+----+----+----+----+----+----+
| 10 | 11 | 20 | 21 | 22 |23 | 42|
+----+----+----+----+----+----+----+
| 9 | 12 | 19 | 18 | 17 | 24 | 41 |
+----+----+----+----+----+----+----+
| 8 | 13 | 14 | 15 | 16 | 25 | 40 |
+----+----+----+----+----+----+----+
| 7 | 30 | 29 | 28 | 27 | 26 | 39 |
+----+----+----+----+----+----+----+
| 6 | 31 | 32 | 33 | 34 | 35 | 38 |
+----+----+----+----+----+----+----+
| 5 | 4 | 3 | 2 | 1 | 36 | 37 |
+----+----+----+----+----+----+----+
Edited on November 30, 2005, 11:47 pm
Edited on November 30, 2005, 11:53 pm
checkmate (spoiler)
