Lenny Conundrum

Every week, The Neopets Team releases a new Lenny Conundrum puzzle, and each week that puzzle gets posted on our blog. You can discuss with others the answer in the comments and come up with a solution! We also discuss the Mystery Picture Answers aswell!

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Thursday, March 08, 2012

Lenny Conundrum - Round #443

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!

46 comments :

  1. I got 2930 but I don`t know if it's right.

    This is what I did:

    Assuming you can re-use numbers to get the amount of possible combinations it would be 75 x 75 x 75 x 75 which gets you 31640625, the amount of possible combinations. Each combinations takes 8 seconds so 31640625 x 8 = 253125000 total seconds spent doing combinations. There are 86400 seconds in a day so 253125000 / 86400 = 2929.6875 which rounds to 2930 days it would take to try all the possible combinations. Thoughts?

    ReplyDelete
    Replies
    1. lol well 0 can be a part of secret code too .. so u have to consider 0 as well which sums upto 76

      Delete
  2. it sounds about right, considering you had no errors in the math. maybe wait for some other people to put theyre answers here?

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  3. there would be 76 combinations, since it's 0-75.

    ReplyDelete
  4. Does 0 Count in a safe combination?

    ReplyDelete
  5. I got 6178.

    The numbers are 0 to 75, which means there are 76 different numbers. 76 x 76 x 76 x 76 = 3,362,176. The problem also said she didn't know which way to turn first, and you can either start clockwise or counter-clockwise, so I multiply by 2 and get 66,724,352. Multiply by 8 seconds, and I get 533,794,816. Divide by 86,400, and I get 6178.18074, which rounds to 6178.

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  6. The puzzle said 3 or 4 digit combinations. Need to have 76*76*76.... too?

    ReplyDelete
  7. er won't 3 by covered by 4 too -- try the three combo first, then add the fourth digit? What worries me more is whether it makes a difference if you go all left or all right or alternate between them. Does that make a difference to the unlocking process?

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  8. Can you use two numbers in a row when cracking a safe?

    ReplyDelete
  9. 'er won't 3 by covered by 4 too' The answer would be no.

    ReplyDelete
  10. but you don't know if it's 3 or 4 digits

    ReplyDelete
  11. This puzzle is too ambiguous. We don't know if numbers can repeat. We don't know if the person will do 3 numbers and then start over.

    ReplyDelete
  12. don`t forget the right and left side =)

    ReplyDelete
  13. Agreed. There are too many assumptions in this week's puzzle. Of course that means, TNT can just make up any answer and have that be the "correct" one.

    ReplyDelete
  14. well u have to count 0-76, 3 and 4 times as there could be possible of 3 or 4 numbers.. so we have to calculate with 3 as well as 4 number combination too.. so i guess it wud be 76*76*76 + 76*76*76*76...

    opinions now

    ReplyDelete
  15. We have to consider combinations for 3 numbers as well as 4 numbers!

    You'll have 76 choices for the 1st number.

    Assume that you cannot re-use the same number (very logical, if not how would the lock work if all 4 numbers are the same!) 75 for 2nd, 75 for 3rd, 75 for 4th.

    Since each number can be reached by turning either direction, so multiply by 2 for each number!

    Total combi: (76*75*75)*2^3 + (76*75*75*75)*2^4
    Total time taken: Total combi * 8
    No of days = (Total combi * 8) / 86400 = 47816.666 = 47817

    ReplyDelete
    Replies
    1. its easy for the lock to work with the same numbers...ex: 0000, turn to 0,go one full circle back to 0,then another full circle to 0, then one last full circle to 0. :)

      Delete
  16. I agree with above answer except that...
    not sure about 2^3 and 2^4
    I just used 2
    I don't think you can turn clockwise and then clockwise again, in my very short experience with safes (couldn't open them even knowing the right combination) you have to alternate directions, so it only make a difference which one you start.

    ReplyDelete
    Replies
    1. Agree!

      Total combi: (76*75*75)*2 + (76*75*75*75)*2
      Total time taken: Total combi * 8
      No of days = (Total combi * 8) / 86400 = 6016.666 = 6017 days!

      Delete
    2. you can turn them same way twice or more.... my lock's like that

      Delete
  17. I just answered 4. I'm just taking a guess, because i don't think it would take her that long to figure it out.

    ReplyDelete
  18. Can numbers repeat? Does 0 count? If you try a 4 number combination, does that cover a 3 number combination?
    If the answers are yes, yes, and no, I got 6260.
    2(76^3+76^4) for the number of combinations. Converting to days rounds up to 6260.

    ReplyDelete
    Replies
    1. your answer sounds right

      Delete
    2. Haha, what kind of bullshit is that? I got the right answer but apparently they want you to round DOWN. That isn't exactly how it really works.

      Delete
  19. 2(76*3 + 76*4) = 1064 combinations. Each takes 8 seconds, so multiply.
    8512 seconds total. 60 seconds in a minute, so divide, and you get 141.8666666666667 minutes (I'm not going to round until the end)
    60 minutes in an hour, divide again, and you get 2.364444444444444
    so I got 2.4 hours. I can't see any mistakes I made at ALL, and now I'm really friggin confused. Is it a trick question? Does it not ACTUALLY take [days] like they said?
    ugh

    ReplyDelete
    Replies
    1. It is obvious that your answer is wrong!

      The first line is already wrong. It should not be 2(76*3 + 76*4), instead if you want to count like this should be 2(76^3 + 76^4). This means 76 cube(76*76*76*) plus 76 to power 4 (76*76*76*76).

      But I believe 2(76^3 + 76^4) would also be wrong...

      Delete
    2. 76*3 = 76 + 76 + 76, and you really should multiply, not add.

      8(2(76^3+76^2))/60*60*24

      Delete
    3. I'm confused, now. Why would you do 76 * 76 * 76? That's doing 0-75 each 76 times.
      The way I did it, you have 76 possible choices for the first number. then another 76. then another 76.
      So that's adding. If you 76^ then it's doing each possible number 76 times, but there arent 76 combination slots, there are 3.
      Friggin
      i always hated this part of math x_x

      Delete
    4. OK let's go to something simple to explain.

      You have 4 balls, w, x, y, z.
      You have 4 numbers, 1, 2, 3, 4.

      How many ways can you choose 1 ball and then 1 number?

      Answer: 16 (which is 4*4 and not 4+4)

      w1 (means choosing w then choosing 1)
      w2 (means choosing w then choosing 2)
      w3, w4, x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4 (Total 16 unique ways)
      _____________

      So now we extend the concept to the question.

      If you have 76 numbers, and you want to choose 1 number out of these 76 and then 1 number again out of these 76, how many ways are there?

      So for the first number there are 76 choices.
      So for the second number there are 76 choices again (assume allow repetition).

      Thus 76*76 and not 76+76

      Delete
  20. I hate math, so I'm here looking at your answers. I find the whole thing dumb because she ends up cracking it anyways at the end of the story... Does that mean it took her no days at all? Least fun conundrum yet.

    ReplyDelete
  21. ((76*76)*76)+(((76*76)*76)*76)
    (5776*76)+((5776*76)*76)
    438976+(438976*76)
    438976*33362176
    33801152S

    (((33801152/60)/60)/24)
    ((563352.5333333333/60)/24)
    (9389.20888888888889/24)
    391.217037037037

    391 Days

    ReplyDelete
    Replies
    1. WOW.... did you like advanced math or something... i think your correct...

      Delete
    2. how the hell is simple dividing and adding advanced math

      honestly

      Delete
    3. You forgot the 8 seconds part?

      Delete
  22. Permutations, order matters

    nPr(76,3) (choosing 3 numbers out of 76 where the order matters) = 421800
    nPr(76,4) (choosing 4 numbers out of 76 where the order matters) = 30791400

    multiplying each by 8, you respectively get 3374400 and 246331200, and the sum of those = 249705600
    divide by 60 to get from seconds to minutes, 60 again to get from minutes to hours, and then by 24 to get from hours to days, gets you 2890.1111111111, or 2890 days when you round.

    ReplyDelete
  23. Lol Answers are all over the place

    ReplyDelete
    Replies
    1. has anyone got a trophy yet

      Delete
  24. where is everyone getting the number 76 from it doesn't have it on the question it has 75.

    ReplyDelete
    Replies
    1. 1 to 75 = 75, plus 0 = 76

      Delete
  25. I've only seen one correct answer on here..
    And the math is quite simple actually.

    2 [(76 x 76 x 76) + (76 x 76 x 76 x 76)]
    ^This gets you how many possible combinations.

    Then times it by 8 which gets you how many seconds total. Proceed to divide by how many seconds are in a day (86400.)

    Round that final number and you get the answer.

    ReplyDelete
  26. First, isn't it possible that the numbers in the combination repeat, so 76 nPr 3 = 438976 and 76 nPr 4 = 33362176. Second, it says she didn't know which way to turn the dial first, so wouldn't you have to multiply by 2 to account for starting each possible combination in a different direction? Then multiply by 8, divide by 60, divide by 60, divide by 24.

    ReplyDelete
  27. The answer was 6260

    ReplyDelete
  28. You won the Lenny Conundrum! First 250!

    6259 :)

    ReplyDelete
  29. No one knows the new one?

    ReplyDelete