Monday, July 6, 2015

A little puzzle

Those of you who like puzzles and problem solving, try out this New York Times puzzle. I'll put my result in the comments. 


  1. I put in about 8 tests and guessed the answer correctly.

  2. Good for you! are you on management side in Big pharma by any chance? if not, you should apply to switch roles! maybe we need some folks like you up there.

    1. Lol, those who have met me in real life know that I am as dumb as a box of rocks.

  3. So did you intentionally test sequences that you hypothesized would give a "No"? I expect that most scientists would, since our training helps us understand the value of negative results. I generated four or five nos and five or six yeses before entering my correct guess.

    1. I sensed/intuited there was a trick, so I tried to get "nos" before I guessed.

    2. When I read the challenge, it put me in mind of a book I read years ago called "The Logic of Failure" which made me suspect that the rule might be an exponential sequence (one of the author's findings was that humans are hard put to conceptualize exponential phenomena, which certainly seems to ring true as far as government is concerned).
      I ran several sequences that I thought might reveal "no" answers, including sequences involving ones, zeroes, negative integers, and real numbers - also I tried reversing positions in some sequences - revising my hypothesis as I went.
      Eventually I thought I had it, and was right vis. the first two numbers, but I fell into the trap of thinking there was necessarily a different mathematical relation between the first two numbers and the third.

    3. All too often in med chem I've seen people get just a couple pieces of data that kind of make sense, and then they think understand the SAR much more deeply than they actually do, and they avoid making a lot of compounds on the basis of "that obviously won't work." I always throw in a few analogs that I don't think will be active--most of the time they aren't, but sometimes they are and we learn something interesting that can potentially take the series in a new direction. The challenge, as in most of life, is the balance. Don't make too many dead compounds, but don't miss things by thinking your models are more robust than they really are.

    4. I didn't get it right because I assumed it was harder than it was (and because I wasn't certain if the sequences had to be increasing else they would terminate, but that was wrong and irrelevant because there were only sets of three numbers - the rules didn't have to generate infinite sequences), but I was trying to get "no" answers because I couldn't get anything useful out of the correct answers. So I failed, but for the wrong reason. Not sure it helps.

  4. Me too (with about the same number of test answers). I wonder if scientific thinking and hypothesis forming are useful in getting to the right answer in this puzzle?

  5. I ran ten tests, four of which returned No before submitting my answer.

  6. 6 tests. First 3 were right so I tested with 3 wrong answers before submitting and getting it right.

  7. I fell for the trick. Run five tests with a "x2" hypothesis, got all "yes" and didn't care to get to a "no" before checking the answer. Next time .... :)

  8. Derek Muller from the Youtube channel Vertiasium does a great bit on this, it's basically the exact same test:

    Unfortunately it spoiled the surprise for me!

  9. I figured it out in one guess but that was only due to the fact that I follow Veritasium on youtube.

    Warning: Spoilers

    This same idea was put to the test in this Veritasium video with the same rule. He states that the video was inspired by The Black Swan by Nassim Taleb.

  10. Here’s a list of every possibility I checked.

    Ascending order
    Ascending absolute value
    Each number double the previous number
    Each number double the absolute value of the previous number
    Second number greater than the first
    Third number greater than the first
    Third number greater than the second
    Second number greater or equal to than the first
    Third number greater than or equal to the first
    Third number greater than or equal to the second
    Numbers in reverse alphabetical order
    Number of letters in number names increasing
    Number of vowels in number names increasing or staying constant
    Numbers in alphabetical order based on the last latter in their names
    Numbers names have English homonyms
    I also confirmed that ascending order worked for absurdly large positive and negative numbers in order to ensure there were no range restrictions.

    Needless to say, I had a lot of No’s. Does anyone have some other hypotheses as to what the answer could be other than "ascending order"?

    1. I forgot to include the obvious "All even numbers". It was the first thing I checked actually.

      Hmmmm....I wonder what the minimum number of required tests is to sort through all these possibilities is? You can eliminate anything related to doubling or language by replacing 8 with 10, for example. It was kind of a pain to check all the possibilities related to absolute values, greater than vs greater than or equal to, and whether all three rather than just two numbers mattered. I had about a dozen tests, around half No's and Yes's, but probably could have been more efficient if I thought it through in advance.

    2. I completely missed a very distinct hypothesis, though my first two tests (2-4-10 and 1-2-4) inadvertently eliminated it. Could you guess what this hypothetical rule was, based on the following chart?

      2 4 8 Pass
      2 4 10 Fail
      1 2 4 Fail
      3 4 8 Pass
      0 4 8 Fail
      2 4 193569 Pass
      2 4 193571 Fail
      2 6 8 Pass
      -2 4 8 Pass
      2 -4 8 Pass
      2 4 -8 Pass
      2 9 -8 Pass
      0.2 0.4 0.8 Pass
      0 8 193569 Pass
      2 4 193571 Fail
      9 88 193569 Fail
      99 193569 88 Pass

    3. A lot of these options can be eliminated by using just prime numbers.

    4. I need a project code so I can work on this some more. That the one with 193569 passes but replace it with 193571 fails is hurting my brain...

    5. Hint:

      7235213 = 0
      49660 = 5
      8 = 2

    6. Are you sure about the:
      0 8 193569 Pass
      otherwise I would have an idea....

    7. 0 8 193569 passes.

      So does Franklin Delano Roosevelt. But George Walker Bush? Definitely a fail.