Miracle Island
(Published on 29. December 2024, 07:29 by apiyo)
Place the digits 1 to 5 once each in every row and column, as well as on the marked negative diagonal.
Digits joined by a white dot are consecutive.
Digits joined by a V sum to 5.
Not all clues are given.
Draw a Whisper line through the middle of some cells to create a single enclosed loop in the grid which visits every row and column at least once. The line moves only diagonally, and must not intersect or cross itself. Neighbouring digits on the line must differ by at least 2.
Our grid today is a desert island inhabited by 25 stranded Digitfolk, each sitting in their allotted cell. The island is ruled over by an all-seeing, all-knowing tyrant, who has forbidden any form of communication between our castaways. Any hint of communication, and the lot of them will be divided by 0 and discarded into oblivion.
The years of captivity and silence have taken a toll. And what with the murky waters offering no reflection, not a single Digitfolk can even remember her own value any more. Each can see that everybody else is a digit from 1 to 5, but can't help but wonder if they themselves might be unique... "Am I perhaps a 6?" one wonders. "Surely I must be a million or more, no doubt about it!" boasts another to himself. One takes solace imagining herself as the eponimous castaway of The Life of Pi, destined some day to emerge back into the world after so many dark and stormy days cast adrift, free to once again calculate radii, poke fun at Tau enthusiasts, and bathe in the dumbfounded admiration that her supreme irrationality inspires in one and all.
One thing is certain though, and they all know it: these Digitfolk are one clever mob. Each is a perfect logician, only ever taking an action when absolutely certain of the outcome. This shared understanding of each other's logicality keeps hope alive that some day they'll find a cunning path to freedom.
One fateful evening, an intreprid Solver sails into harbour to offer a lifeline. Quite the riddler, even in these dire circumstances, from the prow of your ship you proclaim:
"I see at least one 5 amongst you! Now, if you know your value, join me on my ship! If you remain unsure, never fear... I shall return each evening and welcome anyone who has determined their truth!"
On which evening will you welcome your first Digitfolk aboard? Count to this cell in the grid, reading left to right, top to bottom. The digit in this cell is the count of Whisper cells in the 9 cells centred on this cell. (For clarity, evening number 1 is the evening of your proclamation.)
On welcoming your first guests, you bellow "Ahoy ye logical mateys, welcome aboard! Now, for those of you who remain stranded, my ship has plenty of room for you! So hear this: I see amongst you at least one odd digit! Now, if you know your parity, join us aboard! If you remain unsure, never fear... I shall return each evening and welcome anyone who has determined their truth!"
How many evenings will it take you to welcome your next guests? Count to this cell, continuing through the grid from the first cell you identified. The digit in this cell is the count of Whisper cells in the 9 cells centred on this cell.
"Ahoy ye odd folk! Welcome! And to all those left stranded, my sincerest apologies are due! My ship has sprung a leak and is not long for this world. But with the help of your learned colleagues, I am sure we can rebuild and rescue you some other time! Toodleloo!"
Note that no guessing, trickery or wordplay shenanigans are required to solve this puzzle. It can be solved purely logically. The logical riddle is very difficult to solve from first principles, whilst the Sudoku aspect is fairly straightforward.
To see a more generic statement of the problem, you can find a good one here https://xkcd.com/blue_eyes.html
Solution code: Digits not on the whisper line in rows 2, 3 and 4, in reading order.
Comments
on 29. December 2024, 19:36 by askaksaksask
This is really clever. I will say, I'm familiar with this riddle and the inductive logic involved--from the xkcd comic to Tao's WordPress series on the riddle--so it was very quick to deduce the right cells. I imagine for someone who hasn't seen the riddle before and tries to solve it on first principles before tackling the puzzle, this would be a 5* puzzle (it is a hard logic problem!) However, someone inclined to read the Tao or the many stackexchange posts on this could probably get very close after some prerequisite familiarity. I liked this, all said. I think 4* is a fair compromise. Very novel approach either way. Thank you!
on 29. December 2024, 12:09 by apiyo
Minor edits to rules.
on 29. December 2024, 11:58 by lmdemasi
When one first looks at the instructions on this page, it is easy to think that the rules part ends with "It can be solved purely logically. - - - - -" Many people add thematic non-rules text to their puzzles in a similar fashion, so it is easy to misunderstand what is happening here.
I suggest making it clearer that there are rules in the rest of the text.
Once I read the rest of the text and understood what was happening, I enjoyed the puzzle.
-- thanks for the tip, lmdemasi! Glad you enjoyed the solve.
