How Can You Guess That?

I am an honest person, and am thinking of one of three numbers: 1, 2 or 3. You may ask me EXACTLY one yes-no question, I will answer truthfully, and if you chose the right question, you will know which number I’m thinking of!

Communicated by Rob Andler.

76 Comments

  1. Steven Miller on July 31, 2017 at 2:22 pm

    email me at [email protected] for a hint



  2. Guest on July 31, 2017 at 9:05 am

    May I ask what his answer was?



  3. Steven Miller on December 14, 2015 at 2:33 am

    o: meow meow ima cat ([email protected]): Please email me at [email protected] to discuss your soln.



  4. Steven Miller on August 3, 2015 at 6:48 pm

    Jim Sansone: email to you bounced. Your answer to 1,2,3 is one of the best I’ve seen. .s ([email protected])



  5. Steven Miller on December 19, 2012 at 1:51 pm

    But you only have ONE question (sjm1 AT williams.edu)



  6. Anonymous on December 19, 2012 at 11:24 am

    very easy
    is your number 1? (Yes)
    is your number 2? (No)
    is your number 3? (No)



  7. Steven Miller on November 14, 2012 at 9:45 pm

    I don’t see why this works — sjm1 AT williams.edu



  8. Anonymous on November 14, 2012 at 2:37 pm

    is it in the middle



  9. Steven Miller on October 30, 2012 at 3:32 am

    that doesn’t work -=- 1 is considered a unit and not prime (sjm1 AT willilams.edu)



  10. Steven Miller on October 30, 2012 at 3:29 am

    this sadly doesn’t work:: 1 and 2 are both ‘no’s’ — sjm1 AT williams.edu



  11. Steven Miller on October 30, 2012 at 3:28 am

    This doesn’t work — sqrt(0) and sqrt(-1) are both no’s (sjm1 AT williams.edu)



  12. Anonymous on October 29, 2012 at 11:09 pm

    I have an even better answer than my previous:

    Is the square root of the number two below your number odd? (If n=your number, is sqrt(n-2) odd?)



  13. Anonymous on October 27, 2012 at 12:23 am

    Is the number two above it odd and the number two below it positive?



  14. Emily on October 26, 2012 at 3:21 am

    Is the number prime?



  15. Steven Miller on September 22, 2012 at 3:50 pm

    yoav: email me at sjm1 AT williams.edu for solns / discussions



  16. Steven Miller on September 7, 2012 at 12:58 am

    well phrased! sjm1 AT williams.edu



  17. Steven Miller on August 24, 2012 at 12:45 am

    Lukas: correct! you can email me at sjm1 AT williams.edu



  18. Steven Miller on August 10, 2012 at 1:25 am

    sergio: love the phrasing, one of the best I’ve seen; email me at sjm1 AT williams.edu if you want to chat more.



  19. Steven Miller on July 14, 2012 at 8:03 pm

    doesn’t work as 1 is a unit and not prime, so if the number is 1 or 2 you answer no. email me at [email protected] to discuss more //s



  20. Lusine on July 14, 2012 at 6:30 pm

    Is the number prime and greater than 2 ?



  21. Steven Miller on July 1, 2012 at 1:58 am

    I don’t understand: sjm1 AT williams.edu



  22. Amel Okicic on June 30, 2012 at 1:52 pm

    *only smaller (sorry)



  23. Steven Miller on June 1, 2012 at 8:53 pm

    email me (sjm1 AT williams.edu) how this works. If it’s 3, 2, or 1 what do you get?



  24. lil prince on June 1, 2012 at 8:52 pm

    Is the number 2 smaller than the number your thing of, but grater than 1??



  25. Steven Miller on May 29, 2012 at 3:53 am

    the key word is ‘sometimes’



  26. Michael on May 29, 2012 at 3:48 am

    Written by Steven Miller on April 12, 2011.Reply
    Hint: you need to find a question which, even though one is trying to get the other person to say yes or no, is such that sometimes neither yes nor no is appropriate.

    I saw you wrote this, so I was trying to ask a question that was a (yes or no) but still neither (yes or no) is appropriate.



  27. Steven Miller on May 29, 2012 at 1:21 am

    I don’t see how this works. //[email protected]



  28. Michael on May 28, 2012 at 11:49 pm

    is it the number I’m thinking of?



  29. Steven Miller on May 17, 2012 at 10:35 am

    doesn’t matter if it takes a long time — they can figure it out. actually, isn’t too bad. 3 divides the number if and only if it dividesthe sum of digits. doesn’t divide.



  30. jake on May 17, 2012 at 7:39 am

    Ask “Is the number a factor of 4856423”. If they are thinking of 1 they will say yes cos one goes into everything, if they are thinking of two they will say no cos the number is odd, if they are thinking of three they will either say i dont know or will take a long time to work it out.



  31. Steven Miller on May 11, 2012 at 3:03 am

    if they answer no then it’s 1 or 3 but you don’t know which



  32. Anonymous on May 10, 2012 at 11:59 pm

    Is it an even number?



  33. Steven Miller on May 2, 2012 at 1:21 pm

    This isn’t a yes/no question: try to rephrase and send to me at sjm1 AT williams.edu



  34. Truman P on May 2, 2012 at 1:17 pm

    I would ask: If you subtract 2 from the # that you are thinking, is the solution positive or negative?



  35. Steven Miller on April 29, 2012 at 3:31 pm

    email sjm1 AT williams.edu



  36. janaki on April 29, 2012 at 2:01 pm

    give me a hint



  37. Steven Miller on April 17, 2012 at 4:50 pm

    but why can’t I say “no” if I’m thinking of 2 dogs. If I’m thinking of 2 dogs, I’m not thinking of more than 1 cat.



  38. ncn on April 17, 2012 at 4:37 pm

    Convert 1,2,3 into 1 cat, 2 dogs and 3 cats. Ask the question “Are you thinking of more than one cat? Yes means 3, No means 1, silence means 2.



  39. Steven Miller on April 12, 2012 at 6:23 pm

    more please — divided by 2 what? email me at sjm1 AT williams.edu



  40. Ann on April 12, 2012 at 4:45 pm

    Is the number divided by 2 ?



  41. Steven Miller on April 2, 2012 at 12:56 am

    I dont’ think this works — email me at sjm1 AT williams.edu to chat more.



  42. yuval on April 1, 2012 at 10:28 pm

    witch of your answers(yes or no) has the number of letters that it is the number you are thinking of? that way, if it’s one, he cant answer it



  43. Steven Miller on March 28, 2012 at 2:24 pm

    correct. As 1 is not a prime, it cannot be an even prime. As 3 is odd, it cannot be an even prime. Thus, your question has two NO answers (1 and 3) and only one YES answer (2).



  44. xiaomilk on March 28, 2012 at 2:03 pm

    1 isn’t a prime. Prime numbers are numbers divisible by 1 and itself. So it has 2 factors. But 1 is a number with only 1 factor and isn’t considered a prime. If the answer was no then the answer would be 3; 2 if the answer was yes. Am I right?



  45. Steven Miller on March 28, 2012 at 11:36 am

    not quite == 1 and 3 are both non-even primes, so you’d say no for both.



  46. xiaomilk on March 28, 2012 at 8:24 am

    Is your number an even prime number?



  47. Steven Miller on February 4, 2012 at 1:58 am

    to awesome: I think you’re on the right track but there are some grammar mistakes and your answer isn’t clear. Email me at [email protected]….



  48. awesome on February 4, 2012 at 12:06 am

    okay,
    so if you take your number and take away 1, then divide your number by the number that is one less that it, is the answer an even number?



  49. Steven Miller on January 26, 2012 at 4:00 am

    To whomever posted with f(x) — not quite sure if that works, as (x-3)/(x-3) is often replaced with 1.



  50. Steven Miller on January 25, 2012 at 12:29 am

    Johnny: correct: not posting as it’s the soln. Well done. /s



  51. Steven Miller on December 11, 2011 at 2:13 am

    This isn’t a yes/no qusetion; this is just a question with three answer.



  52. Andrew on December 11, 2011 at 1:02 am

    If i was to subtract one from the number you chose how many positive numbers would I have to choose from? If it is 1 the answer would be 1. If it was 2 the answer would be none and if it was 3 the answer would be 2.



  53. Steven Miller on November 1, 2011 at 12:07 pm

    you’re welcome



  54. mukuro on November 1, 2011 at 11:44 am

    oh, yes!!! thank you!



  55. Steven Miller on October 30, 2011 at 1:17 am

    mukuro: correct! not posting as it’s the answer.



  56. Steven Miller on October 20, 2011 at 1:00 am

    Aldo: correct



  57. Steven Miller on October 18, 2011 at 1:24 pm

    I don’t see how this will work. If the person says ‘no’ then you’re stuck.



  58. William Fox on October 18, 2011 at 6:07 am

    Soo many ideas so few answers. Lets go with. Will you tell me your number?



  59. Steven Miller on October 3, 2011 at 1:36 pm

    I prefer not to post the solns online, as that ruins the fun for some people as they might accidentally see the answer before they’re ready to see it. Email me at [email protected] for the soln. .s



  60. Mads on October 3, 2011 at 12:12 pm

    awaiting answer



  61. Steven Miller on September 29, 2011 at 7:31 pm

    I don’t think this quite works.



  62. ANT on September 29, 2011 at 7:00 pm

    Is the number you’re thinking of larger than 1 and smaller than 3?



  63. Steven Miller on September 13, 2011 at 5:04 pm

    close but not quite



  64. Ben Colten on September 13, 2011 at 4:13 pm

    The answer I came up with a long time ago, when I solved this problem was, “I’m thinking of 2 numbers. One of them is 1. The other is either 2 or 9. Is the number you’re thinking of one of the numbers I’m thinking of?”



  65. Steven Miller on September 4, 2011 at 2:10 am

    not quite — I’d answer ‘no’ if my number were 1 or 2, as 0 is not positive.



  66. ts on September 3, 2011 at 8:08 am

    If you subtract 2 from your number, is the result positive?



  67. Steven Miller on June 22, 2011 at 1:59 am

    I don’t think this works. You say yes if it is 3, but you say no if it is 2 or 1.



  68. Prasan on June 22, 2011 at 1:18 am

    The number you are thinking is an odd no greater than 1.



  69. Steven Miller on April 16, 2011 at 9:06 pm

    The problem with this is that if the number is 1 you say no, but if it is 2 or 3 you say yes and thus you cannot distinguish b/w 2 and 3.



  70. Steven Miller on April 16, 2011 at 9:04 pm

    If the number was three you would answer ‘no’; if the number was two you would answer ‘yes’, but if the number is one you would also answer ‘no’ as that number is NOT greater than one.



  71. John on April 16, 2011 at 4:39 am

    Is the # 3 or an even # ?



  72. John on April 16, 2011 at 3:51 am

    Is the number you’re thinking of greater than 1 but smaller than 3?



  73. Steven Miller on April 16, 2011 at 2:48 am

    You’re on the right track. If the number is 3 you would answer no; however, if the number is 1 or 2 you would answer no.



  74. User lne on April 16, 2011 at 2:35 am

    Is the number 2 smaller than the number you are thinking of?



  75. Steven Miller on April 12, 2011 at 3:17 pm

    Hint: you need to find a question which, even though one is trying to get the other person to say yes or no, is such that sometimes neither yes nor no is appropriate. If this doesn’t help, email me at [email protected].



  76. masai williams on April 11, 2011 at 6:11 pm

    what is the answer?



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