Master Bomb Defusers

Question

Day 115 of your investigation and you and your ever-faithful-if-only-a-bit-slow partner have finally caught the trail of your arch-nemesis, a serial bomber known only as "Mr. 5".

Doing your best to hold back snide remarks about terrible cliches, you step into the abandoned warehouse located near the center of a busy city and wonder why super-villains never pick 5-star hotels as their hideouts, or better yet, the upstairs room of a decent pub. At least then you could enjoy a nice pint during the all-too-traditional monologue sequences.

All beer-related thoughts quickly disappear as you spy the mountain of explosives capable of relocating your body parts several miles apart.

"Good news Watson!" you exclaim.

"My name's Derek, sir" comes the feeble reply of a man desperately trying to cling to a sense of self-identity.

"And how many times must I say it?" you interrupt, "Derek is no name for a sidekick!"

"You mentioned good news?" sighs the yet-to-be-renamed sidekick.

"Ah yes" you reply, reminding yourself not to experiment with hallucinogenic frogs before next interviewing for sidekicks, as it clearly lowers your standards.

"If we position ourselves exactly 91cm from the explosives and jump precisely into the air, the majority of our body pieces should be blown Eastward into the flat, through the window I conveniently opened this morning before we left"

"How exactly is that good news?" sighs John...? No... that's too unoriginal. Bruce? No... now he sounds like an Australian who wears uncomfortably short shorts and drives a pickup truck. How about Sean...? Hmmm... he may end up dying sooner than you'd like, so perhaps not...

"Think of how much we'd save in cab fare!" you say, as super-ultra-mega-sidekick (patent pending) rolls his eyes at you and then leans in to get a better look at the explosive device.

If you are reading this, then at last the game is finally afoot! However, it would be no fun to beat you so early in the match, especially given you have the power of two minds, so I shall start you off simple...

The password to defuse the bomb is: 31 63 107 107 ? 119 24 124

I'm afraid I can't give you the 5th number, but I'm sure you'll figure out why. I thought about using 91, but I wouldn't want you to misinterpret my intent.

I've given you 9 minutes to enter the correct password because it's not possible to give you any longer...

The display above the device flickers on and displays the number "111" alongside a keyboard containing only letters

"It appears to be a rather crude cipher" you muse aloud.

"We need to solve it fast!" exclaims the stater-of-the-obvious, "Time is against us!"

The display suddenly flashes, the number changing to "37"

Surely it can't have been more than 2 minutes since we started! you think to yourself

You stand in ominous silence, wondering if you've got enough money left for a drink tonight.

The display flashes again, this time displaying "123".

"Oh!" you shout, "so that's how it works!"

You study the device for a moment, content in your new discovery.

"For shame!" you say condescendingly after a moment. "Having such a basic password for such a device. I do hope our next outing will be capable of at least outsmarting my grandmother! It's not even a complete cipher!"

"So what's the password?" asks the still-unnamed man.

"Why don't you try all by yourself?" you jest. "But I'll tell you what, if it gets to '36', I'll put the password in myself, but the rounds are on you tonight"

The display changes to "107" as the man besides you gulps, all-too-familiar with your post-victory drinking habits...

What is the password?

Hint 1

Use the countdown as your starting point

Hint 2

Both the password (which we know must be only letters) and the countdown timer (which we know must be only numbers), make use of "107"

Hint 3

In what scenario can you display all of the numeric digits (0 - 9) and most (but not all) of the letters of the alphabet?

Notes

• You might be able to "brute force" the password, but I will only accept a response that includes an explanation of how the password was found
• Bonus points: why is it not a "complete cipher"?
• This is my first attempt at incorporating a story + some humour into a puzzle, so I apologise if it's a little dry! It is mostly intended as flavour, but there are a few hints here and there
• There are a couple of "Easter eggs" scattered throughout the puzzle and although I can't award anything for them, feel free to include them in your answers if you picked up on them!
• There are two really obscure references which tie into the story, if anyone can pick up on them, I'll be really impressed (I'd award rep for it if I could)

Answer 1

The password is:

password

as @sylux said (Hint 3):

the numbers correspond to a 7-segment digital display

The encryption system works this way:

First you transform the number to binary. For example: 107 -> 1101011. If the binary number is less than 7 digits long, add zeros to the left.

Then

The 7 positions correspond to the 7 segments displayed with 0 being (light off) and 1 being (light on), in this way:

where 1 refers to the leftmost binary digit and so on.
For example, in the case of 107 (1101011) we can see it this way:
bottom: 1 -> on
bottom right: 1 -> on
bottom left: 0 -> off
middle: 1 -> on
top right: 0 -> off
top left: 1 -> on
top: 1 -> on
which gives the display of a 5 (or S)

By applying this principle, we get:

111 = 1101111b = 9
37 = 0100101 = 7 (here it appears that 8 was skipped, probably they didn't pay attention when the display changed to 127).

The countdown continues similarly:

123 = 1111011b = 6
107 = 1101011 = 5
and finally
36 = 0100100 = 1

The same principle applies to the password:

31 = P
63 = A
107 = S
? = ? (if it was 91 = E)
119 = O
24 = r
124 = d
By grouping the previous letters, the only word satisfying pass_ord is password. Also, if he used 91 (E) it would can be interpreted as a rotated W. from the story, "but I wouldn't want you to misinterpret my intent".

This is an incomplete cipher because:

you cannot represent all the letter with it. (v, w, k etc)

Some hints in the text:

"If we position ourselves exactly 91cm from the explosives and jump precisely into the air, the majority of our body pieces should be blown Eastward into the flat, through the window I conveniently opened this morning before we left"
You can see letter E in "Eastward" capitalized where 91cm -> E

Answer 2

So with the above hints, my start of an answer:

A bit backward way of solving it but:

If the characters are shown on some amount of 7-segment displays, then 'W' would not be a possible character. Hence leaving it out of "password".

Also

If the numbers correlate to the password then that would mean 107 is probably both '5' and 'S' which fits with hint #2

And finally

The cipher seems incomplete because if 9 minutes displays as '111' and presumably 5 minutes displays as '107' then only 2 numbers are displayed in-between, thus one minute's display was skipped or the interval is not one minute.

Answer 3

Mhmd absolutely nailed it with a great explanation, but I thought I'd collect all the hints and references into one place.

One interesting note...

When I originally put the puzzle together, I labelled each of the "segments" with a power of two (1, 2, 4, 8, 16, 32 and 64) going from top to bottom, left to right. Mhmd used a slightly different approach, but still reached the right answer!

Extra Hints

Mhmd already picked up on it, the 91cm (91) corresponds to Eastward (E) in the cipher

"super-ultra-mega-sidekick" - the first letter of each word spells "SUMS", which is how the numbers in the cipher are made (by summing powers of two)

"especially given you have the power of two minds" - power of two is hidden in that dialogue, hinting at the need to use base 2 (aka binary)

Easter Eggs

"Good news Watson!" - Watson was of course the faithful sidekick of Sherlock Holmes

"sighs John...? No... that's too unoriginal" - John was the first name of Dr. Watson

"How about Sean...? Hmmm... he may end up dying sooner than you'd like, so perhaps not..." - a large number of characters played by Sean Bean (the actor) usually end up dying, often fairly early on (GoT and LotR are classic examples)

I do hope our next outing will be capable of at least outsmarting my grandmother! - the older generation aren't exactly known for the technical prowess and many still use "password" as their password

The really obscure references

Both references are in the opening paragraph, which refers to the serial bomber.

"Day 115" - 115 is the corresponding value for 'G' in the cipher. Fans of the Hunter X Hunter anime/manga series might recognise the name 'Genthru' as "The Bomber" from the Greed Island arc

"Mr .5" - 'Mr. 5' is the name of the Baroque Works Officer Agent in the One Piece anime/manga series, whose Devil Fruit gives him the ability to make parts of his body (namely his boogers) explode

Yes, I like anime/manga... Deal with it :)