You have been captured by small cute puppy.   He has two identical opaque vases, and 100 white beads and 100 black beads.  The puppy will allow you to arrange all of the beads in whatever way you like between the two vases, but neither of the vases can be empty.  The puppy will then close his eyes, put his little paw into one of the vases, rummage around, and remove just one bead.  You have no idea which vase he will choose.

If the puppy chooses a black bead, you will be allowed to stroke his head.  But if he chooses a white bead he will bite you.  How do you arrange the beads to give yourself the best chance of getting a stroke?

As ever, please do NOT post your answers, but feel free to say if you solved it and how long it took.  Solution (and credit for the puzzle) on Monday.

104 comments

  1. Three minutes, most of the time was spent confirming the result w/ brute force. Of course, puppies can’t grab a bead with their paw. 🙂

    This puzzle is open to several trick solutions.

  2. Is there a place where we can ask questions? It seems like there is an extremely simple way to keep the undesirable beads from the puppy, but it seems so obvious its like cheating.

  3. “How do you arrange the beads to give yourself the best chance of getting a stroke?”

    Have someone throw them at your head.

    1. @nappi no just shrink and clone yourself and you and your clone get into the vases and the cute puppy will stroke your head when it reaches in to pick a bead…..simple once you are able to shrink and clone yourself and with all the cleaver ones here should only take about 20 seconds….. but if you are wanting to stroke the puppy’s head….well you’ll have to work out the puzzle….. :}

  4. 2 – 3 minutes of thinking about probabilities has given me an answer that I’m fairly sure of, but I’ll have to wait until Monday to find out. Thanks, Richard, for giving us a break from those sadistic prison guards. I wonder how many comments will complain that the puzzle makes no sense because puppies don’t have opposable thumbs?

    1. Re-reading the question after morning coffee and with a more alert brain, I can see an ambiguity in the language that allows for a trivially easy answer. I hope that isn’t the one we are supposed to get.

  5. Whethervor not the pup pick up the bead depends on the size of the beads and size/shape of his paws. If he has a moderately tight arrangement of pads and a deep cleft between he should have no problem with a bead large enough to wedge in.
    As for the original puzzle I’m still trying to work out how to arrange beads between the jars whilst still leaving at least one in each. I never get these either but it’s fun to try and keeps the brain alive!

  6. I immediately thought of two answers – one a literal interpretation of the language used to set the task, and the other concerning probabilities and the length of puppy legs! I will be interested to see the reveal on Monday.

  7. This seemed so easy maybe I’m wrong – had it before I finished reading it. Can’t be that simple can it or am I just getting the hang of doing these?

  8. Seen this one before. The first time i did this puzzle it took me about a minute.

    But I don’t like dogs, so I’ll just ignore him.

    and “You have no idea with vase he will choose.”: with should be which

  9. As I have a fear of all cats and dogs, I could never be locked in a room with said puppy from Friday until the solution is published on Monday.

    So…

    Kill the puppy!

    (Cue lots of Hate messages). Remember folks, it is hypothetical. I could never kill a real puppy, unless in self-defence, such as if it tried to bite me. I would hope that waving my 2 walking sticks at the puppy would keep it at bay.

  10. The best solution I can think of can reduce my chance of getting bitten to around 25%. While without any strategy, the random chance would be 50%. I am still thinking if more improvement can be made,

    1. I think you are giving the answer away 😦

      If on the other side, you had said that the three first decimal digits on the probability of not being bitten of the solution were 874, then you had show you knew the solution only to those who already knew it too… without giving anything away.

    2. And if you had said that the first decimal digits on the “probability of not bitten” were 874, you may have written them in the wrong order!?

    3. I didn’t have the solution until I read these comments here… the specificity of the probability really gave it away for me, or at least led me down the right path.

    4. C’mom, are you saying that my 874 gives the solution away more than to say it is slight less than 75%? You are joking!

    5. I was thinking of solutions in the area of how to distribute the beads evenly amongst the vases in a way that your average puppy would be more likely to pick a black bead (eg, put all black beads on top). With this sort of solution, someone might say they have a 75% chance of winning; but nobody would put the odds to three decimal places.

      To be fair, others had talked about calculations… this might have equally led me to the correct solution if I’d taken them seriously.

  11. It took me about 5 minutes including reading some of the comments to reveal the most likely answer, knowing that it’s not a trick question or to do with the fact that there is a dog involved.

  12. I convinced myself that this is a straightforward math problem, regardless of the obfuscation.

    I had to first overcome the notion that the distribution would not matter – “Overall, it’s always 100 beads out of 200, right?” No! Then I had a hunch, and I confirmed it with a back-of-the-envelope calculation and a brute-force perl loop.

    About 15 min total.

  13. This problem is delicious. Awesome. I only needed a few seconds to pass from the obvious objections to the obvious right answer, but even so, beautiful.

    Credits on Monday means his author is perhaps here? Maybe this is the fable dragon puzzle 🙂 After all the expectations, is the only puzzle worth them.

  14. Okay, the puppy was misleading, but as soon as I read the 100 white & 100 black marbles & 2 vases, I knew what puzzle this was. I know the answer and understand why it’s correct.

  15. Within a few seconds I’d got one answer, based on probability.

    After reading the comments, I’d got a second, based on a strict reading of the criteria (and noting the absence of one possible criterion which, if it existed, would invalidate this method)

  16. You have been captured by small cute puppy. .. so i don’t deserve anything better than, the Dogs biting me.

    Actually, i dont like any dogs… so i will not want to touch the beast…

    Ohterwise the solution of the optimizing task was easy… and under one 1 minute

  17. I had an idea that gave an answer of 25% of picking black. The problem with my answer is that it also gives a25% chance of picking white. But these add up to a 50% chance of picking a bead. Obviously there is a 100% chance of picking a bead so if your percentage for black and white don’t add up to 100% you’ve made a mistake.

  18. I believe I have the correct solution. Took me about 3 mins, I also thought of a bit of a “trick” solution, although I think its in line with all the rules that were stated.

  19. You wrote “You have beem captured by small cute puppy”. Please change this to “a small cute puppy”. You forgot the A.

    Also, how in hell would you be captured by a puppy anyway? Really, arrange it so you gets bitten, you deserve it.

    Also, how does the puppy pick the beads up with a paw?

    Also, “How do you arrange the beads to give you the best chance of getting a stroke?”? Really? I laughed at that. Really, who want to get a stroke? Sure, you may want to stroke it, but you dont wanna get a stroke. You would die.

    Also, I think it took about 5 sec to solve. It was quite simple.

    But, also, some additional ways to solve it:
    1: Puppies are slow, just put the beads in random, if it gets a white bead, just run as hell

    2: It wont be able to pick up anything using its paw, because paws are not made for that, making it impossible for it to choose anything to do with you, and it must let you go

    3: Again, how do you get captured by a small, cute puppy? If a puppy is able to do that, you wont be able to lift the beads anyway, and I am surprised you are not dead by now. So you are either dead, or you never got captured. Problem solved.

    (PS: I guess these are not the solutions that you were looking for, but they are way bether to use in real life…)

    1. You’re clearly missing a factor. The puppy, using its mind-altering cuteness, has recruited minions that have captured you and brought you to their master. So it has captured you, but in the same way that E.S. Blofeld captures James Bond. By proxy.

      This, by the way, also means that it is a lose-lose puzzle. Either you get bitten, or you get cuted into becoming a mindless minion.

  20. Okay I’ve got one answer which is dependant on the language used in the question being a bit wibbly on a certain point and I’ve got another more mathematical answer which as I suck at maths, probability and all that is probably wrong – took me about 5 mins once I sat down and concentrated.

  21. I wasn’t sure it this was a probability test, or knowing Richard, some kind of psychological test. If it’s probability, I have it. Took about 30 seconds.

  22. I came up with three possible answers. One is physically based, and the wording of the question fairly much eliminates it. The second is mathematically based, and seems to be the answer that a few other people have gotten. The third one leaves me with a 100% chance of stroking, but is most likely cheating.

  23. Solved it by the third sentence! This is too easy! The answer is in the text! Please give the solution to see if I am indeed correct!

  24. Ah, a PC puzzle. The black bead is the desirable one! Maybe it’s about time we also changed the rules of chess and have the player with the black pieces start first.

  25. Assuming that I can’t just chuck all the white beads out … a little creative thinking (not usually my style) leads me to think I have the best solution in about 30 seconds.

  26. Got it as soon as I read it. I sure hope the correct answer isn’t a play on words or have any thing to do with the fact that dogs can’t speak nor pick up beads.

    1. Well lilabyrd says if wrong she can just fly away, where as joshthelegend will just be standing around hoping people will be talking about him for years to come while said cute puppy is chewing on his ankle….. :}

  27. I have the answer that I guess is the same as JB and Herbert, since I calculate a probability of 74.75%

    But given the previous rubber band thing, I guess it could be something like “arrange 50 black beads in one vase, 50 black beads in the other vase, and 100 white beads in outer Mongolia”

    1. Not the same fraction as I have, but close. If you retrace the steps you took to arrive at your result, perhaps you can find a correction.

  28. Think i got it… in three minutes. Im not shure the 20 second solution of some other volk here is correct, think again !

  29. Took me about half a second to think of a solution, a minute of reading the comments to come to the conclusion that I had been a little too loose with my semantics, and another half a second to find the loophole in that logic. Both solutions give a 100% chance of getting to pet the small cute puppy.

    –Dave

  30. Coming to this late, but eventually had an “Oh yes, of course” moment after about 2 mins. Some of the comments here help make me sure I have the right answer based on probability. My first thoughts were too tied up with the physics of how beads in a vase would behave I you rummaged through them and hence how you might influence the selection that way-still possible in reality I think but I prefer the solid logic of the probability answer-although perhaps by combining the two…

  31. Thought of a solution but it wasn’t obvious to me that it was optimal, so I checked it using algebra and a spreadsheet (my calculus is rusty!). Seems to work! Took me about a minute to get it, but a further ten minutes to check it, at least 🙂

  32. I got the same answer intuitively as others here in a few minutes, but the problem is, how do I prove it? Hoping to get some insight on Monday!

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