Faster Lock Combination
Difficulty:
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Over on Steampunk Island, Bow Ninecandle is having trouble opening a padlock. Do some research and see if you can help open it!
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Challenge

Hey there! I'm Bow Ninecandle, and I've got a bit of a... 'pressing' situation.
You see, I need to get into the lavatory, but here's the twist: it's secured with a combination padlock.
Talk about bad timing, right? I could really use your help to figure this out before things get... well, urgent.
I'm sure there are some clever tricks and tips floating around the web that can help us crack this code without too much of a flush... I mean fuss.
Remember, we're aiming for quick and easy solutions here - nothing too complex.
Once we've gathered a few possible combinations, let's team up and try them out.
I'm crossing my legs - I mean fingers - hoping we can unlock this door soon.
After all, everyone knows that the key to holiday happiness is an accessible lavatory!
Let's dive into this challenge and hopefully, we won't have to 'hold it' for too long! Ready to help me out?

Solution

I watched the HelpfulLockPicker video three times to follow the steps exactly. Another good video explaining the methodology can be found here.
According to the video we want to find the sticky number and the two guess numbers.

Step 1: Finding the sticky number

We are going to turn the lock clockwise several times to reset the lock (by double clicking the dial).
We put some tension on the shackle and pull up until it seizes the lock and let off a bit so we can start turning the lock (the tension status color must be brown).
Now we're going to turn the dial clockwise and keep turning until the dial stops on a number. We repeat this a few times to find 12, where it stops.

Step 2: Finding the Guess Numbers

These are going to lie between 0 and 11.
We are applying heavy tension to the shakle (tension status color must be red) and turn the dial to find a position where it's going to sit in the middle of two half numbers.
The first guess number is 3. The second guess number is 10. For all other positions it doesn't stop in the middle of two numbers.

Step 3: The Math
Part A: Finding the first digit

Sticky Number: 12
12 + 5 = 17, so 17 must be the first digit.

Part B: Finding the third digit

First digit was: 17
17 / 4 = 4 with remainder of 1 (4 is always constant for all locks)

Guess numbers were: 3 and 10
We're adding ten to each
3 - 13 - 23 - 33
10 - 20 - 30 - 0
These are possible combinations for the lock
To find now the two possibilities we divide each of these numbers by 4 and note the numbers with the same remainder of 0:
13/4 = 3 rem. 1
33/4 = 8 rem. 1
So these numbers may be a third combination of our lock.
We are further reducing the possibilities by turning the dial to those numbers and applying heavy tension to the shakle again.
33 feels a lot looser than 13 so 33 must be the third combination.

Part C: Finding the Second Digit (8 Possibilities)

We're adding 2 to our remainder and add 8 to it 4 times:
3 - 11 - 19 - 27 - 35
We're adding 2+4 to our remainder and add 8 to it 4 times:
7 - 15 - 23 - 31 - 39
The second and the third digit need to be greater than two away so we can eliminate 31 and 35.

Step 4: Testing it out
  1. digit: 17
  2. digit: 3 - 7 - 11 - 15 - 19 - 23 - 27 - 39
  3. digit: 33

Let's try all those possibilities:
Important: pass the 2nd digit once! (see the following image):

2023_Faster_Lock_1.jpg

Cool, successful at the first attempt: 17 - 3 - 33

2023_Faster_Lock_2.jpg

Bow Ninecandle adds
Oh, thank heavens! You're a lifesaver! With your knack for cracking codes, we've just turned a potential 'loo catastrophe' into a holiday triumph!