Uzarro is quite good at theiving and the various activities that go along with such a hobby. Sneaking? Yeah, awesome. Jumping through lasers? Pfft. Cracking safes? Piece of cake.
One night she was so bored of the average heist that she decided to give herself a challenge. She was attempting to crack a safe in the basement of a wealthy shopkeeper - one who'd recently increased security measures by... well, a lot. After making it past all the other tricks and traps, she reached the safe.
The challenge? She hadn't done any research on this model. She wasn't sure if there were three numbers in the combination, or four. She also wasn't sure which direction to turn the dial first. The only thing she did know was that the dial had numbers from 0 to 75.
She briefly considered how long it would take to try all possible combinations, one by one, knowing that each sequence would take her 8 seconds on average. Did we mention she was good at maths? Because she is, and she chuckled at the answer before using her crazy skills to bust the safe open and hightail it out of there.
How many days would it have taken her to try every possible combination, rounding to the nearest day?
Submit the answer without spaces or punctuation or you will be disqualified!
I got 46875.
ReplyDelete(150*150*150*150)*8/60/60/24
I dunno. I might have gone wrong somewhere.
I'm pretty sure that it's (76*75*75*75*2*8)/60/60/24
ReplyDeleteBecause each number after another cannot be the same number in the combination
Forgot to mention that it's 0-75, which means there are 76 numbers.
DeleteIt said she didnt know which direction to turn the dial. So it'd be double (75 left or 75 right).
ReplyDeleteAlso. If the pointer is at zero, there are 75 other numbers it could be (in any one direction).
also, it says she doesn't know if there are 3 or 4 numbers in the combination
ReplyDeleteI'm pretty sure this is a Permutations problem..
ReplyDeleteSo what i did was (76 ^3) + (76 ^4) * 8 = 270409216 seconds / 60 seconds per minute = 4506820.266 minutes / 60 minutes per hour = 75113.6311 hours /24 hours in a day = 3129.73629 rounded to 3130 days
But he time would be different, wouln't it?
DeleteI think i messed up because i didn't consider that the dial can go left or right :(
ReplyDeleteBut it can only go left or right for the first number. Then it would have to alternate.
DeleteAre we to assume that the lock pops open as soon as the right combination is entered? After she tries a 3 digit combination, can she just add another number for a 4 digit one, or does she have to start a new combination?
ReplyDeleteBut as you work out the 4 number combination, you are also working out the 3 number combination in the same calculation.
ReplyDeleteWhat I did was {(76^3)*2 + (76^4)*2}*8 then take that answer divide by 60, divide by 60 again then divide by 24. The answer I got was 6259.47
ReplyDeletebut if the 1st number is not 0??
Deletethen it would be {(76^2*75)*2+(76^3*75)*2}*8 and all divided by 60 then 60 then 24...
And that's 6177 days.
answer is 6259.
ReplyDeleteone day - the answer is one day !!!
ReplyDeleteI feel it is unthinkable to have a combination that uses the same number twice, so I posit it should be
ReplyDelete(76*75*74*73*8)+(76*75*74*8)/60/60/60=2890
However, I reserve the right to be wrong, LOL.
As usual the ambiguity in the lack of clarification on these conundrums can create some uncertainty, making it even harder than simply "doing the math".
oops, that shoud have be /60/60/24, my bad
DeleteYou also forgot to add a *2 since the combination can begin turning left or right (then alternating)
DeleteSo it should be:
((76*75*74*73*2*8) + (76*75*74*2*8))/60/60/24
Or to simplify:
(((76!/72!)+(76!/73!))/5400 = 5,780
Note: 1/5400 = 16/(60 * 60 * 24)
This is assuming the combination can not have more than 1 instance of each number (Similar to the Dice conundrum they gave us a few weeks back), this ALSO assumes that the lock does not automatically open if the combination is 3 numbers, thus not allowing a 4th number to hit two combination with one try.
Yes, this seems insanely high for a one-night break-in.
Well I understand your math, but I also feel logic is relevant. So .... if you have ever opened a combination lock you may recall that to start you must turn counterclockwise at least one complete revolution and stop at 0. Therefore to begin trying all combinations to unlock, you would turn clockwise first (after starting cc at 0) and then stop at the first number in the combination and so on. So I chose to ignore the 2 based on how a combination lock works in real life
DeleteI also maintain that you simply would not ever have a combination that repeats a number, in fact I am not even sure the tumblers would fall if you did that. That said ambiguity is probably going to bite me in the a** since logic may not rule in a Lenny Conundrum and the calculation may well allow a number to repeat in the combination as was the case in the dice puzzle. The difference IMHO is that in the Dice puzzle you can obviously have a number repeat in a real life situation.
6259
ReplyDeleteFrom reading the problem, I assume that you can (1) use each number more then once (2) start with 0 {thus the default 0 0 0 combo would work} (3) the choices of right and left are only applicable in the beginning (ie you don't have to factor in right or left for each individual number, just once for each combo) (4) you can't combine 3 and 4 digit combinations (all 4 combos do not include 3 combos).
ReplyDeleteIn other words I assume the safe works like this: (Right or Left)(1st 0-75)(second 0-75)(third 0-75)(Pull) OR (Right or Left)(1st 0-75)(second 0-75)(third 0-75)(fourth 0-75)(PULL)
If all these assumptions are correct then the math should be [(76^3)+(76^4)]*2*8/60/60/24 ; where 76^3 is all the 3 digit combos, 76^4 is all the 4 digit combos, 2 is right or left, 8 is seconds per combo, and the rest is to convert seconds to days.
Answer is 6259.
as someone posted above the answer is one day. if it was more than one day the owner would be back and she would be caught. making you do the math is a trick.
ReplyDeleteif so ,the answer should be 0 instead of 1 .
Deleteas long as she only do it in night ,i.e. less than 12 hours ,in the morning the shopkeeper will be back .
rounding off the answer to nearest day ,less than 12 hrs means less than 0.5 day ,so ,the answer won't be 1 .
"How many days would it have taken her to try every possible combination, rounding to the nearest day?"
DeleteThey say WOULD IT HAVE TAKEN HER!!!! Learn to read.
It's not 1 and it's not 0. It says 'would it have taken her' doesn't mean that's what she did, because it said she briefly tried it, but that is what you have to calculate.
ReplyDeletedang ! I was sooo close 3129.7 * 2 = 6259.4 arrrg. Stupid left and right!
ReplyDeleteI got 6178
ReplyDeleteyou can figure out all 3-digit combinations while trying the fours. This would then be 76^4 (76 possible numbers you can have at each part of the 4-digit code). Times 2 because you can start either left or right. Times 8 for the total second she needs to try each combo. Divided by the total of 86400 seconds in a day.
(76^4 * 2 * 8)/86400 = 6178
Question???? Is the 6259 and 6178 the days it would have taken her.
DeleteI dont know how I did, but I sumbitted 13 days :S
ReplyDeleteI really think we should consider the 6259.4, because in the final question, it says to consider the rounding to the nearest day :)So the answer would be 6259.
ReplyDeletei got 2854 days BITCH!!!!!!!
ReplyDeleteYou da bitch - it's one day fool !!!
ReplyDeleteAll you people with the right answer are so stupid!! Why the hell are you telling everyone else the answer!! Give hints, not the actual answer.
ReplyDeleteGo away if you don't like it. The name of the site is Lenny Conundrum ANSWERS!!!!!!
DeleteCan someone plz tell me what the right answer is theres quite a few going around
ReplyDelete1. assume dial start at number x. 76 choices. [76]
ReplyDelete2. 2 directions to turn now - left or right. [76*2]
3. you'll stop at one number eventually.
4. now you WILL have to turn in opposite direction.
5. assume the same number is not used, you have 75 choices [76*2*75]
6. you'll stop at one number eventually.
7. now you WILL have to turn in opposite direction.
8. assume the same number is not used, you have 75 choices [76*2*75*75]
3-combinations: 76*75*75*2
Do this for 4 combinations and you'll get: 76*75*75*75*2
So total combinations: 2 ( 76*75^2 + 76*75^3 )
Total time = Total combinations * 8 seconds
Days = Total time / (24*60*60)
You will get Days = 6016.6667 = 6017 days