Faster Lock Combination

Faster Lock Combination

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

Solution

Even though not listed as a hint, Bow Ninecandle itself provides the link to a very good youtube tutorial named “[198] Close Up On How To Decode A Dial Combination Lock In 8 Attempts Or Less”, which I basically followed before going ballistic 🙂

The first digit

By applying some tension so as to have the “Tension Status” indicator looking brown, I determined $13$ as the sticky number, with $4$ and $7$ being the guess numbers. To obtain the first number then: $n1 = sticky + 5 = 13 + 5 = 18$.

The third digit

A little more math gives us the remainder to watch out for $r = n1 / 4 = 18 / 4 = 4 R 2$. Based on the guess number, we can write down a table such as the following:

GUESS NUMBER	$4$	$4 + 10 = 14$	$4 + 20 = 24$	$4 + 30 = 34$	$7$	$7 + 10 = 17$	$7 + 20 = 27$	$7 + 30 = 37$
REMAINDER	$4 / 4 = 1 R 0$	$14 / 4 = 3 R 2$	$24 / 4 = 6 R 0$	$34 / 4 = 8 R 2$	$7 / 4 = 1 R 3$	$17 / 4 = 4 R 1$	$27 / 4 = 6 R 3$	$37 / 4 = 9 R 1$

Elegible third digits are the ones for which remainder matches $r$, the one obtaining by divinding $n1$ by $4$:

• $14$
• $34$

By applying the tension and further verifying the two eligible numbers, $14$ looked more promising being the loosest, but I also kept $34$ just in case.

The second digit

To obtain the second digit is used the below table:

Row 1 - $Remainder + 2 = 4$	$4 + 0 = 4$	$4 + 8 = 12$	$4 + 16 = 20$	$4 + 24 = 34$	$4 + 32 = 36$
Row 2 - $Remainder + 6 = 8$	$8 + 0 = 8$	$8 + 8 = 16$	$8 + 16 = 24$	$8 + 24 = 32$	$8 + 32 = 40$

Eliminating those being 2 digits apart from the third digits, below the list of attempts:

• $n1 = 18$, $n2 = (4, 8, 20, 24, 32, 34, 36, 40)$, $n3 = 14$
• $n1 = 18$, $n2 = (4, 8, 12, 16, 20, 24, 40)$, $n3 = 34$

Going ballistic

I swear I tried, but I just wasn’t able to get the lock open, so I started analyzing the JS code, eventually discovering the variable lock_numbers which confirmed I had the right digits:

{
	"bad_third_number": 34,
	"first_number": 18,
	"first_number_sticky": 13,
	"guess_number1": 7,
	"guess_number2": 4,
	"second_number": 4,
	"third_number": 14
}

And then I found the function moveLockIntoUnlockedPosition() - which just opened the lock with 0 effort - still it was great to refresh some lockpicking knowledge 🙂