3 ms·

That's exactly what I was thinking. I (sometimes) follow TDD, and I applied it to this problem. I made sure to include negatives, 0, positives, and include prim

That's exactly what I was thinking. I (sometimes) follow TDD, and I applied it to this problem. I made sure to include negatives, 0, positives, and include primes here or there to help avoid issues with multiplication/exponentiation. After a few of these, I felt pretty confident that the rule was simple.

ubernostrum 11y ago
My process was: [3 5 7] [7 5 3] [8 4 2] [5 7 3] [1 2 3] [1 1 1] [0 1 2] At that point I could've done some more to be really certain, but felt confident enough and guessed (correctly).
- jonkiddy 11y ago
  [16 32 64] [0 0 0] [1 2 3] [3 2 1] [-1 0 1] [3 5 7] [-2 -1 0] [111 54231 9999999999999999999999] At that point, I correctly answered the question.
  - jws 11y ago
    Similar to mine, but we both actually failed. Real numbers are accepted and we did not test that.
    - WildUtah 11y ago
      It accepts floating point numbers. To approximately double precision. But it accepts zero percent of real numbers.
      - eru 11y ago
        I can nitpick better than that! To talk about a certain fraction of real numbers you have to have a distribution over them. In general we take the uniform distribution if no distribution is explicitly given. That doesn't work for real numbers (it doesn't even work for natural numbers). (See https://math.stackexchange.com/questions/14777/why-isnt-there-a-uniform-probability-distribution-over-the-positive-real-number https://math.stackexchange.com/questions/14777/why-isnt-ther...) If there's no implicit default distribution, we have to pick on. I can pick one where they cover an arbitrary high percentage of real numbers..
        elnion 11y ago
        Down the rabbit hole of pedantry: we don't need a distribution, just a measure, if we want to talk about how many reals it accepts. The Lebesgue measure is implied on the Reals if none is given, and the computable reals have measure zero. We can't reasonably talk about a percent coverage, since the Lebesgue measure of the reals is infinite, but as a non-technical description, 'zero percent' is morally equivalent to saying it only covers a measure-zero set.
  - profinger 11y ago
    I did this plus also testing [1 1.5 2]
- perlgeek 11y ago
  So you limited yourself to non-negative integers, and had no idea what negative numbers or fractions would do.
  - eli 11y ago
    Based on the context of the question and the UI of the testing interface, fractions seem unlikely to be an intended part of the question. I likewise wouldn't bother testing unicode U+216x roman numerals.
    - Ntrails 11y ago
      It refused to accept both fractions and imaginary numbers. I did test negatives and zeros since that was really the only remaining set I could think of. Most importantly I used about 6 tests (3 right 3 wrong) to come up with the answer and then did another 17 looking for the trick. After all, it couldn't just be that simple right?
  - bbcbasic 11y ago
    Also he didn't know what numbers whose digits add up to 88 would do.
  - __david__ 11y ago
    Their input on the phone wouldn't allow minus or period characters so I assumed positive integers were the set.
  - ubernostrum 11y ago
    The presentation of the problem -- and I know that trusting the problem state is unwise sometimes in cognitive-bias tests, since many such tests are actually designed to be "we said we were asking X but actually meant Y" -- indicated a simple rule, rather than one which would behave differently on different classes of numbers. So after the tests listed above I felt confident enough to guess.
joezydeco 11y ago
Did you try floating point numbers? I didn't see anything in the text that said integers only.
- tptacek 11y ago
  I tried floating point numbers. Also, at 28 decimal places, the test breaks; it's not arbitrary precision. So, technically, the answer isn't simply "any ascending sequence of numbers".
  - deleted 11y ago
    [deleted]
  - SiVal 11y ago
    I actually avoided going that far to avoid getting bad data. I was trying to answer the question, "What does the experimenter THINK his rule is?" rather than what will the computer do. Since the computer can't be infinite, it will inevitably fail with overflow, underflow, and such. I was relieved, in fact, when it worked with negatives and floats in a "safe" range. I also tested with 1,1,2 and 1,2,2 to make sure that the required increase applied to ALL of the values, not just a specific pair.
    - mjevans 11y ago
      I too tried to test if it was only one pair that was significant. However I grew impatient and didn't try to come up with more tests when I thought I had a sufficient answer to explain my most vexing observation (negative, positive, positive out of combinations involving negative numbers). The observation to brainstorm for ways of proving that a statement is in fact wrong, and exhausting them, is such an eloquent way of wording the hunt for a negative.
  - joezydeco 11y ago
    Hah! Nice catch.
    - 11y ago
rahimnathwani 11y ago
I was a little less systematic, but still had a positive:negative ratio of 1:2 before I submitted my answer. 4,6,8 Y 1,1,1 N 1,2,3 Y 1,6666,8777 Y 1,0,1 N 3,2,1 N 3,2,3 N 5,6,4 N 7,5,6 N

ubernostrum 11y ago

My process was: [3 5 7] [7 5 3] [8 4 2] [5 7 3] [1 2 3] [1 1 1] [0 1 2] At that point I could've done some more to be really certain, but felt confident enough and guessed (correctly).

jonkiddy 11y ago
[16 32 64] [0 0 0] [1 2 3] [3 2 1] [-1 0 1] [3 5 7] [-2 -1 0] [111 54231 9999999999999999999999] At that point, I correctly answered the question.
- jws 11y ago
  Similar to mine, but we both actually failed. Real numbers are accepted and we did not test that.
  - WildUtah 11y ago
    It accepts floating point numbers. To approximately double precision. But it accepts zero percent of real numbers.
    - eru 11y ago
      I can nitpick better than that! To talk about a certain fraction of real numbers you have to have a distribution over them. In general we take the uniform distribution if no distribution is explicitly given. That doesn't work for real numbers (it doesn't even work for natural numbers). (See https://math.stackexchange.com/questions/14777/why-isnt-there-a-uniform-probability-distribution-over-the-positive-real-number https://math.stackexchange.com/questions/14777/why-isnt-ther...) If there's no implicit default distribution, we have to pick on. I can pick one where they cover an arbitrary high percentage of real numbers..
      - elnion 11y ago
        Down the rabbit hole of pedantry: we don't need a distribution, just a measure, if we want to talk about how many reals it accepts. The Lebesgue measure is implied on the Reals if none is given, and the computable reals have measure zero. We can't reasonably talk about a percent coverage, since the Lebesgue measure of the reals is infinite, but as a non-technical description, 'zero percent' is morally equivalent to saying it only covers a measure-zero set.
- profinger 11y ago
  I did this plus also testing [1 1.5 2]
perlgeek 11y ago
So you limited yourself to non-negative integers, and had no idea what negative numbers or fractions would do.
- eli 11y ago
  Based on the context of the question and the UI of the testing interface, fractions seem unlikely to be an intended part of the question. I likewise wouldn't bother testing unicode U+216x roman numerals.
  - Ntrails 11y ago
    It refused to accept both fractions and imaginary numbers. I did test negatives and zeros since that was really the only remaining set I could think of. Most importantly I used about 6 tests (3 right 3 wrong) to come up with the answer and then did another 17 looking for the trick. After all, it couldn't just be that simple right?
- bbcbasic 11y ago
  Also he didn't know what numbers whose digits add up to 88 would do.
- __david__ 11y ago
  Their input on the phone wouldn't allow minus or period characters so I assumed positive integers were the set.
- ubernostrum 11y ago
  The presentation of the problem -- and I know that trusting the problem state is unwise sometimes in cognitive-bias tests, since many such tests are actually designed to be "we said we were asking X but actually meant Y" -- indicated a simple rule, rather than one which would behave differently on different classes of numbers. So after the tests listed above I felt confident enough to guess.

joezydeco 11y ago

Did you try floating point numbers? I didn't see anything in the text that said integers only.

tptacek 11y ago
I tried floating point numbers. Also, at 28 decimal places, the test breaks; it's not arbitrary precision. So, technically, the answer isn't simply "any ascending sequence of numbers".
- deleted 11y ago
  [deleted]
- SiVal 11y ago
  I actually avoided going that far to avoid getting bad data. I was trying to answer the question, "What does the experimenter THINK his rule is?" rather than what will the computer do. Since the computer can't be infinite, it will inevitably fail with overflow, underflow, and such. I was relieved, in fact, when it worked with negatives and floats in a "safe" range. I also tested with 1,1,2 and 1,2,2 to make sure that the required increase applied to ALL of the values, not just a specific pair.
  - mjevans 11y ago
    I too tried to test if it was only one pair that was significant. However I grew impatient and didn't try to come up with more tests when I thought I had a sufficient answer to explain my most vexing observation (negative, positive, positive out of combinations involving negative numbers). The observation to brainstorm for ways of proving that a statement is in fact wrong, and exhausting them, is such an eloquent way of wording the hunt for a negative.
- joezydeco 11y ago
  Hah! Nice catch.
  - 11y ago

rahimnathwani 11y ago

I was a little less systematic, but still had a positive:negative ratio of 1:2 before I submitted my answer. 4,6,8 Y 1,1,1 N 1,2,3 Y 1,6666,8777 Y 1,0,1 N 3,2,1 N 3,2,3 N 5,6,4 N 7,5,6 N