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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Wednesday, September 07, 2011

Lenny Conundrum - Round #419

Lawyerbot was attempting to organise his Usuki collection and came upon a box with 63 Deluxe Angel Usukis and 113 Devilish Usukis inside. He also had an additional 72 Devilish Usukis next to him in a bag. Then, his programming went a bit haywire.

Every time he'd reach into the box, he'd pull out two Usukis. If they were different, he'd toss a Deluxe Angel Usuki back in. If they were the same, he'd toss a Devilish Usuki back in. He kept doing this until there was only one Usuki left in the box.

Which Usuki was it?


  1. Is there a formula for this?

  2. Deluxe Angel Usukis

    It's simple. The rule state if two dolls are the same they get chuck out + extra stuff. But think of the 63 Deluxe Angel Usukis
    . The last one will not have a pair (because it's odd) and will never be chuck out. Thus the answer is Deluxe Angel Usukis

  3. This is what I just posted in another forum..

    Doesn't really make sense at the moment, but it's 50/50 unless there is some other twist to it.
    Here is what I speculate:
    If they were different, the angel one gets tossed back in.
    But if they were the same, the devilish one gets tossed ... what if he drew out two angels instead of two devils? there is no devilish one to toss back into the box, so he would have no choice but to keep both angels... or would both Angels go back into the box? And although it mentions the extra devilish Usukis in a bag, it clearly says "every time he'd reach into the BOX". I assume that we don't include the extras in the bag at all.
    Discounting the ones in the bag, there are 176 in total.
    Angel + Angel = approx. 18% (still trying to work out whether both angels are sorted or both go back into the box)
    Angel + Devil = approx. 36% chance
    Devil + Devil = approx. 32% chance
    There is a higher chance of two same ones being chosen [(angel + angel) + (devil + devil)] , so a devil would be tossed back into the box more often.

    The odds favor the Devilish Usuki being left, but I am not entirely sure if I'm on the right track with this.


  4. Ah, damn it see it now
    odd numbers - angel

  5. Every time he'd reach into the box, he'd pull out two Usukis. If they were different, he'd toss a Deluxe Angel Usuki back in. If they were the same, he'd toss a Devilish Usuki back in. He kept doing this until there was only one Usuki left in the box.

    What is this nonsense about chucks out??
    Also there is an odd number of Devilish Usukis as well so you fail

  6. it's devilish usuki. there are more of them, just a simple addition problem!

  7. Is that the best answer we all got.

  8. yes, I just noticed that too! both have odd numbers
    but two of the same have to be drawn out for an angel usuki to be sorted
    ..going by that pattern, there would have to be an even amount for all the angels to be drawn!

  9. the more I think about it... definitely angels

    ah dang it! already put devilish :(

  10. Hello everyone. My niece plays Neopets and showed me this problem.
    The answer is definitely Deluxe Angels Usuki (is that how you spell it?) because there is an odd number of each, so the last pair but include both an Angel and a Devil. Thus, an Angel will be tossed back, leaving us with one Angel.

    Neopets is silly!

  11. in response to ^^math major^^, what if i picked different usukis on the first one?
    one angel and one devil would be tossed out.
    then, you put one angel back in.
    now, there's a net loss of one devil.
    So now lets start the problem again...except there are an even number of usukis in the box.

    btdubs, i put devilish. my method was simply to find which chance was higher: same or different. and proceeded...all the way to Devilish

  12. Devilish Usuki. Either way, the box is full of them.

  13. It's more likely to be devilish because "being the same" can be both angel and both devil, while "being different" can only mean one being angel and one being devil.

  14. Ah, but you're basing the rest of the calculations on the fact that you will never again draw two different Usukis. The likelihood of that is exceedingly small. Thus, one Angel will be added back, plus one loss of Devil. So the answer is still Angel, as I told my niece.

  15. Devilish. easy!

  16. There are 63 Angel Usukis. If you draw one angel and one Usuki, you put back on angel, keeping the # of Angel Usuki's odd. If they are the same, it is either an odd number still or an odd number minus 2, which is still odd. Therefore, if there are only 2 left one must be angel because 1 is an odd number, while 2 is not. Therefore, it would have to be an Angel Usuki.

  17. Is monkey fart the answer?

    in the First minute I jellyneo all the Usskis doll thinking the answer was there. Turns out devilish and angel usukis doll are not real XP

  18. Angel because there could never be an even number of angels left in the box. You start with on odd number. So if you pick two different usukis then the angel is put back in leaving you with how many angels you had before. If you draw two angels then a devil is put in so you are still left with an odd number of angels. If you draw tow devils then the number of angels is not changed. So you must have at least one angel left and it'll never get tossed out, therefore it must be the last one.

  19. I agree with angel

  20. the 72 devilish in a bag don't count.

  21. u guys dont get it.if they r the same he throws a devil usuki in. what he keeps getting two angel usukis? nothing cancels anything out.also, if he keeps getting one of each, he keeps putting back an angel.

  22. since it is a 50-50 chance of players getting it right i figure we will all get 20 np

  23. what is the real answer?
    i'm confused !!!
    somebody help me plsssss

  24. Answer is Deluxe Angel Usuki.

    3 possible results:
    1) take 2 angel, put back 1 devil.
    2) take 2 devil, put back 1 devil.
    3) take 1 angel and 1 devil, put back 1 angel.

    Usukibot take 2 angel in a cycle. He has 63 angel, and it's an odd.

    It's impossible to get the last one angel, so the answer is angel.

  25. * Usukibot take 2 angels in a cycle. He has 63 angels, and it's an odd.

  26. Ok guys, this is the trick. Remember that he has 72 EXTRA DEVIL USUKIS. Therefore, whenever he draws two angels, he removes BOTH of them, and then adds in a devil. So you're ALWAYS going to have an odd number of angels. You start at 63, and you only ever remove two at a time. Therefore, at the end, you have one angel and # devils. The devils all get drawn until there are only one angel and one devil left. Then, the devil gets removed and so the answer is

  27. @Rowan M i agree with angel, but isn't the 72 extra... just that? extra info? I mean I put angel because it made the most sense to me but still.

  28. There would be 31 pairs of Deluxe angel usuki and 1 left over still in the box(Don't think about the Devilish in the bag just yet). Now divide the 113 devilish in the box into pairs and you get 56 pairs with 1 leftover. Now if there are 31 egual pairs of Deluxe Angel Usuki that mean when they are pulled out 31 devilish from the bag would be put in. That leaves a remaining 31 in the bag so subtract 56(Devilish pairs) by 31 and you get 25. That means there are 25 devilish and 72 devilish from bag and 1 angel in the box now. 97 would be total devilish and 1 angel. Since there have to be one different pair at the end and you could add no more devilish, the outcome would be deluxe angel usuki.

  29. Honestly I think it's really stupid the people who are saying it's Devilish, and feel bad for the people who listened.
    The answer is Angel, because there WILL ALWAYS BE AN ODD NUMBER OF THE ANGEL ONES.
    Take out two different, you'll add in an angel---that's still odd.
    Take out a pair of Angels, you'll add in a Devil, but that's still odd for Angels.

  30. don't feel bad if they picked devilish out of ignorance. especially when it's a competition and by getting it wrong, our prize is higher per person.