骰之苦
Die Agony
题目详情
A six-sided die, with numbers written on each of its faces, is placed on the 6-by-6 grid above, in the lower-left (yellow) corner. It then makes a sequence of “moves”. Each move consists of tipping the die into an orthogonally adjacent square within the grid.
The die starts with a “score” of 0. On the Nth move, its score increases by N times the value of the die facing up after the move. However, the die is only allowed to move into a square if its score after the move matches the value in the square. Also, the die cannot be translated or rotated in place in addition to these moves.
After some number of moves the die arrives in the upper-right (blue) corner.
The answer to this puzzle is the sum of values in the unvisited squares from the die’s journey.
解析
Original Explanation
For December’s puzzle, you were asked to figure out which numbers to place on the sides of a six-sided die that would allow it to “legally” travel from the bottom-left to the top-right squares in the grid.
The only labeling of the die that permits such a route is: −3, 9, 5, −9, 7, 9. And the only legal path that successfully travels from the yellow square to the blue square is outlined above. The sum of the unvisited squares (shaded in orange, above) is 1935.
(Of interest, note in the upper grid the placement of the die after the 26th move. Several entries claimed that a path existed through the 452 immediately north of the 317. But to move to that cell would cause the score to increase by 27×9, which is not a legal move. The only legal move is to the eastern 452, as 452 = 317 + 27×5.)
Congrats to those of you who successfully navigated the die area!