Here's the first riddle I invented for Puzzling SE. Hope you'll enjoy solving it.
This story takes place during World War II. A German spy is assigned the task to sneak overnight into a military base near London and steal secret documents of utmost importance.
The documents are kept inside 30 safes of reinforced unbreakable steel, and each safe is protected by a numeric secret code. Therefore the only way to get the documents is to open each safe with the correct code. If the wrong code is entered, the safe will immediately trigger a siren which will alert all military personnel, so the spy has only one try available.
German Intelligence was able to provide the spy with the following information:
First, it looks like the codes were not chosen at random, but instead follow some unknown pattern. Second, they intercepted half of the safes' codes, which they communicate 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 is still unknown. German Intelligence advises the spy to delay the mission until all codes have been discovered; however, the spy believes that the pattern is obvious, as a safe's code appears to be the double of the safe's number.
That same night, the spy enters unseen the military base, finds the safes, silently opens each one of them with the correct code and steals the documents. Everything goes well from safe #1 to #17.
However, when the spy enters the code 36 on safe #18, the safe doesn't open; its alarm triggers, and the spy is captured.
Can you find why? If not, continue reading.
A few weeks later, the military base has sixty more safes delivered. The codes on these safes are programmed following the same pattern.
After the end of the war, the commander of the base is asked by the High Command to compile a list of all safes and codes. He produces the following document:
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 find now how the codes were chosen - and hence why the spy failed?
Hint 1
There is an unique solution for the riddle. Don't try to find overcomplicated formulas. There is more than just mathematics -- in fact, although there is quite a bit of calculations, the mathematics involved are very basic. To crack the code, you'll have to do some lateral thinking.
Hint 2
Language is important. The story takes place in Great Britain because the riddle is related to the English language. The nationality of the spy is irrelevant.
Hint 3
Observe how the British chose the secret algorithm to fool spies. "Code of safe $n = 2 \times n$" is a red herring -- it looks like it is the solution, but is valid only up to safe #29 with the exception of safe #18. The units for each "ten" follow a pattern, but each "ten" breaks the pattern. Where would you find such a pattern?