Tuesday, August 15, 2017

enigmatic puzzle - Hiker's Cabin Mystery | Pt. II



Nice one, @GarethMcCaughan!


Finally, you've gotten into his computer using the password you managed to decode from his clues... but there's another issue! There is a secondary box asking for a six-character passcode (excluding spaces). Fortunately, you found some strips of paper on his desk that will be helpful... enter image description here


You are starting to get anxious about this mystery... better get cracking!




Hint 1




Use the two outside numbers for each group of three to get the inside number in some way...



Hint 2



The code is six characters... An asterisk counts as a character!




Answer



Possibly right answer


To find the number in the middle of a strip,




first take the digit-by-digit differences between the numbers at the ends:
483 672 -> 211
976 132 -> 844
759 324 -> 435
148 381 -> 247
533 215 -> 322
891 467 -> 436
318 649 -> 331
948 682 -> 346

then add up the resulting three digits and divide by 2:
483 672 -> 211 -> 2
976 132 -> 844 -> 8
759 324 -> 435 -> 6
148 381 -> 247 -> 6.5
533 215 -> 322 -> 3.5
891 467 -> 436 -> 6.5
318 649 -> 331 -> 3.5
948 682 -> 346 -> 6.5
and then replace ".5" with "*". The first five lines above then yield the numbers seen in the picture. The last three lines are for the other strips, in the order indicated by the arrows.




This suggests that the required code is



6*3*6* (if I've done my arithmetic correctly).





Certainly wrong answer posted earlier, left here so as not to hide my old mistakes:


I will be astonished if this is the intended answer, but it is consistent with the information provided [EDITED to add: ... no, it turned out not to be, because I'd completely missed one of the provided data points] and it's (I think) a little simpler than RedBaron's answer.


To get from the outer numbers to the inner:




For each number, subtract the sum of the two outer digits from the middle digits. E.g., $(483,672)$ becomes $(1,-1)$. Now subtract the number derived from the larger of the two numbers from the one derived from the smaller, so we get $1-(-1)=2$. Finally, if the result is negative then replace its minus sign with an asterisk and write it upside down. So $(148,381) \rightarrow (-5,4) \rightarrow -9 \rightarrow 6*$.



Thus:



our three mystery paper slips, in the order indicated by the arrows, yield $-5$ (hence 5*), $1$, $13$. Pad everything to two characters (adding a space where the asterisk would go if there were one) and we get the 6-character code 5*1 13.



(An earlier version of this answer had a miscalculation in it, which I have now fixed.)


The most unsatisfactory thing here is of course



that space.




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