Here’s the primary riddle I invented for Puzzling SE. Hope you may get pleasure from fixing it.

This story takes place throughout World War II. A German spy is assigned the duty to sneak in a single day right into a navy base close to London and steal secret paperwork of utmost significance.

The paperwork are saved inside 30 safes of bolstered unbreakable metal, and every protected is protected by a numeric secret code. Therefore the one strategy to get the paperwork is to open every protected with the proper code. If the fallacious code is entered, the protected will instantly set off a siren which is able to alert all navy personnel, so the spy has just one attempt out there.

German Intelligence was capable of present the spy with the next data:
First, it seems just like the codes weren’t chosen at random, however as a substitute observe some unknown sample. Second, they intercepted half of the safes’ codes, which they convey to the spy:

Safe   Code
#1     2
#2     4
#3     6 
#4     8
#5     10
#6     12
#7     14
#8     16
#9     18
#10    20
#11    22
#12    24
#13    26
#14    28
#15    30

The second half of the safes’ codes remains to be unknown. German Intelligence advises the spy to delay the mission till all codes have been found; nevertheless, the spy believes that the sample is apparent, as a protected’s code seems to be the double of the protected’s quantity.

That similar evening, the spy enters unseen the navy base, finds the safes, silently opens every certainly one of them with the proper code and steals the paperwork. Everything goes nicely from protected #1 to #17.

However, when the spy enters the code 36 on protected #18, the protected would not open; its alarm triggers, and the spy is captured.

Can you discover why? If not, proceed studying.

A number of weeks later, the navy base has sixty extra safes delivered. The codes on these safes are programmed following the identical sample.

After the tip of the warfare, the commander of the bottom is requested by the High Command to compile an inventory of all safes and codes. He produces the next doc:

Safe   Code   Safe   Code   Safe   Code   Safe   Code   Safe   Code   Safe   Code
#1     2      #16    32     #31    28     #46   -42     #61    34     #76    46     
#2     4      #17    34     #32    30     #47   -40     #62    36     #77    48    
#3     6      #18    25     #33    32     #48   -38     #63    38     #78    50
#4     8      #19    38     #34    34     #49   -36     #64    40     #79    52   
#5     10     #20    40     #35    36     #50    30     #65    42     #80    25    
#6     12     #21    42     #36    38     #51    32     #66    44     #81    27    
#7     14     #22    44     #37    40     #52    34     #67    46     #82    29
#8     16     #23    46     #38    42     #53    36     #68    48     #83    31
#9     18     #24    48     #39    44     #54    38     #69    50     #84    33
#10    20     #25    50     #40   -54     #55    40     #70    34     #85    35
#11    22     #26    52     #41   -52     #56    42     #71    36     #86    37
#12    24     #27    54     #42   -50     #57    44     #72    38     #87    39
#13    26     #28    56     #43   -48     #58    46     #73    40     #88    41
#14    28     #29    58     #44   -46     #59    48     #74    42     #89    43
#15    30     #30    26     #45   -44     #60    32     #75    44     #90    38

Can you discover now how the codes have been chosen – and therefore why the spy failed?

Hint 1

There is an distinctive resolution for the riddle. Don’t attempt to discover overcomplicated formulation. There is extra than simply arithmetic — in actual fact, though there’s fairly a little bit of calculations, the arithmetic concerned are very fundamental. To crack the code, you may should do some lateral considering.

Hint 2

Language is vital. The story takes place in Great Britain as a result of the riddle is expounded to the English language. The nationality of the spy is irrelevant.

Hint 3

Observe how the British selected the key algorithm to idiot spies. “Code of protected $n = 2 instances n$” is a purple herring — it seems like it’s the resolution, however is legitimate solely as much as protected #29 aside from protected #18. The items for every “ten” observe a sample, however every “ten” breaks the sample. Where would you discover such a sample?