Unusual Suspects

The police rounded up Jim, Bud and Sam yesterday, because one of them was suspected of having robbed the local bank. The three suspects made the following statements under intensive questioning.

  • Jim: I’m innocent.
  • Bud: I’m innocent.
  • Sam: Bud is guilty.

If only one of these statements turns out to be true, who robbed the bank?

Communicated by G. Mejia.

89 Comments

  1. Steven Miller on April 26, 2019 at 7:50 pm

    Your answer, Isaac, is not quite right, but your email address wasn’t valid. email me at [email protected]



  2. Steven Miller on December 4, 2012 at 5:15 pm

    email me at sjm1 AT williams.edu



  3. Mathfan on December 4, 2012 at 4:53 pm

    This is a tricky one



  4. Steven Miller on October 25, 2012 at 4:37 pm

    John: correct (email me at sjm1 AT williams.edu)



  5. Steven Miller on October 18, 2012 at 1:05 am

    email me: sjm1 AT williams.edu



  6. Steven Miller on September 15, 2012 at 1:14 am

    Jib: well done



  7. Steven Miller on September 11, 2012 at 2:02 pm

    gilly: email sjm1 AT williams.edu



  8. gilly on September 11, 2012 at 11:33 am

    Bud is saying the truth; both jim and sam are lying. Jim is the robber and sam is innocent. aince if only.one is saying the truth then both bud and sam together can’t be lying; and both bud and jim cant b lying neither since bud cant b both inocent and guilty.



  9. Steven Miller on September 5, 2012 at 2:53 pm

    there’s another soln (sjm1 AT williams.edu)



  10. Steven Miller on September 5, 2012 at 2:53 pm

    glad you’re enjoying — email at sjm1 AT williams.edu to chat more, can solve this indep of other problems



  11. Dr K on September 5, 2012 at 1:14 pm

    Jim robbed the bank



  12. Sergio on September 4, 2012 at 5:37 pm

    Hello again, steve. It’s a delight browsing through your riddles!
    Mixing this with “How can you guess that?”
    Suspects #1,2,3 : Jim, Bud, Sam. Is suspect #X guilty ? (X is your secret number).
    Maybe you can use this riddle as a hint for the other one ?



  13. Steven Miller on September 3, 2012 at 9:53 pm

    ahh, but there is another answer — email me at sjm1 AT williams.edu



  14. Nathan Bower on September 3, 2012 at 1:18 pm

    Jim



  15. Steven Miller on August 30, 2012 at 4:29 am

    I think it might be harder than you think — email me at sjm1 AT williams.edu to chat.



  16. Christy on August 30, 2012 at 3:17 am

    Jiminy Crickets! This problem should be listed as “extremely easy”, why is it in this category?



  17. Steven Miller on July 29, 2012 at 8:14 pm

    ok, hints sent //s (sjm1 AT williams.edu)



  18. maya on July 28, 2012 at 10:35 pm

    i would like that you give me the answer step by step



  19. Steven Miller on July 1, 2012 at 1:59 am

    ahh, but there can be another soln //sjm1 AT williams.edu



  20. Amel Okicic on June 30, 2012 at 1:16 pm

    if Bud tells true then Sam is definitely guilty , because there are only one robber



  21. Steven Miller on June 25, 2012 at 4:33 am

    There is another soln….



  22. Anonymous on June 25, 2012 at 12:22 am

    Bud because sams statement is true. If only one of these statements turns out to be true, who robbed the bank?



  23. Steven Miller on June 4, 2012 at 6:34 pm

    Alex Irby: I get two of your possibilities as happening



  24. Steven Miller on April 27, 2012 at 6:05 am

    ah, but another interpretation is possible too!



  25. Milind on April 27, 2012 at 4:52 am

    Bud’s statment is true.
    Jim robbed the bank



  26. Steven Miller on April 12, 2012 at 6:48 pm

    another interpretation gives another soln — email me at sjm1 AT williams.edu



  27. Steven Miller on April 9, 2012 at 11:54 am

    ahh, but there can be another soln too



  28. Dominic on April 9, 2012 at 9:40 am

    Firstly, i’l say sam is lying. If sam’s statement is false then buds statement is true. How did sam knw dat bud is guilty. OR.sam and bud comited d crime 2geda, jim’s statement is d only truth. I knw one out of my two hypotheses is true



  29. Steven Miller on March 29, 2012 at 10:01 am

    but can there be another answer / interpretation to the problem



  30. sauravshakya on March 29, 2012 at 8:44 am

    wasn’t my answer correct?
    that Bud is telling the truth so JIM is guilty



  31. Steven Miller on March 28, 2012 at 11:32 am

    ahh, but could there be another soln as well?



  32. sauravshakya on March 28, 2012 at 6:44 am

    Jim



  33. Steven Miller on March 5, 2012 at 2:33 pm

    Ah, but is there another soln? //s



  34. mary hester on March 5, 2012 at 12:43 pm

    The one that said Bud is guilty robbed the bank. He never said he was innocent and Bud was with him therefore they both are responsible.



  35. Steven Miller on March 2, 2012 at 5:27 am

    Just sent you a hint — let me know if that helps. (Actually, the email may’ve bounded — email me at sjm1 AT williams.edu for the hint) //s



  36. Doreen on March 2, 2012 at 2:46 am

    what is the answer



  37. Steven Miller on February 26, 2012 at 6:02 am

    ah, but is there another soln???



  38. Stan on February 26, 2012 at 5:08 am

    Both Jim and Bud robbed the bank, which leaves Sam’s statement true and the other statements false



  39. Steven Miller on February 24, 2012 at 6:51 pm

    Ah, but could there be another soln? //s



  40. arka_Logan on February 24, 2012 at 3:36 pm

    my answer is Jim robbed the bank.
    Consider the case II

    Assume Bud is truthful.
    So
    Bud’s Statement is correct.
    Sam’s Statement is false since he assumes Bud as the robber.
    Jim’s Statement is false as he claims him to be innocent.
    Since Jim’s statement is false , so he cant be innocent.

    Jim robbed the bank



  41. Steven Miller on February 21, 2012 at 8:56 pm

    There are two possible interpretations, two possible solns. ..s



  42. Bones on February 21, 2012 at 6:57 pm

    Could it be that Jim and Bud were lying and Sam was telling the truth?



  43. Steven Miller on February 21, 2012 at 1:58 pm

    To Bones: There are TWO ways to look at the problem. You got one of the two interpretations (the one most people miss).



  44. Steven Miller on February 19, 2012 at 1:39 am

    You’re getting closer, but I don’t think it can be all three…. Email me at [email protected] if you want to run a soln by me.



  45. Anonymous on February 18, 2012 at 10:29 pm

    could it be all three of them? only the Bud is guilty statement is true and since Sam knows about the thing, he must be included too.



  46. Steven Miller on February 18, 2012 at 9:53 pm

    ah, but could there be another soln…..



  47. Anonymous on February 18, 2012 at 5:09 pm

    Sam and Bud robbed the bank, Jim is innocent.



  48. Steven Miller on February 18, 2012 at 4:31 am

    ah, but could there be another soln….



  49. Kristina on February 18, 2012 at 4:09 am

    Jim.
    If Bud’s is true, he is innocent. If Sam’s is false, Bud is innocent. If Jim’s is false, he is guilty. This is the only logical solution.
    Other scenarios:
    Sam’s being true? Bud is guilty. Bud: fasle, guilty. Jim: False, also guilty? But only one can be guilty.
    Jim’s being true? Jim is innocent. Bud: false, guilty. Sam: false, Bud is innocent. That’s an endless contradiction.



  50. Steven Miller on February 10, 2012 at 2:59 am

    ahh, but could there be another soln too?



  51. Adamm Hockman on February 10, 2012 at 2:53 am

    Not sure if I am interpreting this correctly but I believe Jim robbed the bank.

    The one person telling the truth is Bud:
    This means Jim was lying (so he robbed the bank).
    This means Bud was telling the truth (so he is innocent).
    This means Sam was lying (so Bud isn’t really guilty, he’s innocent.)

    Seems straightforward to me. 🙂



  52. Steven Miller on January 26, 2012 at 3:10 am

    Ahh, but could there be another soln?



  53. Geoff Moss on January 25, 2012 at 9:21 pm

    Jim is both a liar and the criminal. Bud told the truth and was innocent; Sam lied and was also innocent. (Or I suppose, technically, he could have also been guilty but was smoother and more cunning than Jim and wasn’t even suspected in the first place, and maybe that’s why he accused Bud rather than proclaim his own innocence).



  54. Steven Miller on January 22, 2012 at 3:02 pm

    could there be another solution? email me at [email protected] to discuss.



  55. Andy Yep on January 22, 2012 at 1:53 pm

    If Sam is true while Jim and Bud are lying, then both Jim and Bud will be guilty. (Not possible as there is only one suspect.)

    If Jim is true while Bud and Sam are lying, then Bud is guilty according to himself while Bud is innocent according to Sam (Not possible due to contradiction)

    If Bud is true while Jim and Sam are lying, then Jim is guilty while Bud will be innocent.

    Hence Jim is the guilty party who robbed the bank.



  56. Steven Miller on January 3, 2012 at 2:36 am

    Ah, but there is another solution as well!



  57. DA Retard on January 2, 2012 at 3:02 pm

    Its simple Sam is telling the truth Bud is guilty



  58. Steven Miller on December 13, 2011 at 9:15 pm

    Could there be another solution?



  59. Anonymous on December 13, 2011 at 9:13 pm

    it was sam because he is the only one trying to make himself look innocent, believing that his friends would frame him, he tried to look for a way out



  60. Steven Miller on December 7, 2011 at 2:11 pm

    I don’t believe it’s possible for all to be innocent, but you’re on the right track.



  61. Kiana and Lane on December 7, 2011 at 2:08 pm

    Is the previous one correct though?

    Could it be possible that NONE of these men are involved? (possibly going too far outside of the box on this one)



  62. Steven Miller on December 6, 2011 at 3:00 pm

    depending on how you view the problem, there are TWO defensible solutions



  63. Kiana and Lane on December 6, 2011 at 2:52 pm

    Lane: Jim did it.

    Kiana: I say that Jim did it either with or without Bud as a possible accomplice.

    Are we both right?



  64. Steven Miller on December 5, 2011 at 1:52 pm

    it isn’t so clear — there is another solution! :]



  65. Thilina on December 5, 2011 at 8:03 am

    it’s so clear: It’s JIM. it’s the only way those statements could work out!



  66. Steven Miller on November 16, 2011 at 5:14 am

    there are TWO answers to this riddles. hint: maybe exactly 1 robbed, or maybe exactly 2 robbed!



  67. Soroush on November 16, 2011 at 12:21 am

    I was about to say that Sam in telling the truth but then you wouldn’t know everyone who robbed the bank since then it would be unknown whether Sam robbed the bank or not.



  68. Steven Miller on November 8, 2011 at 5:36 pm

    correct, but there’s another solution too!



  69. Corbin on November 8, 2011 at 5:22 pm

    Jim, because if Bud statement is true, it would make Sams statement false which would make Bud innocent. And also Jims statement of innocence false.



  70. Steven Miller on November 3, 2011 at 4:47 am

    Is there another solution?



  71. Shreya on November 3, 2011 at 3:29 am

    Jim is lying, he robbed the bank. Sam is lying and Bud is saying truth.



  72. Steven Miller on November 1, 2011 at 6:47 pm

    There is another solution.



  73. Michael on November 1, 2011 at 1:25 pm

    So if Sam’s statement is true, then Bud is lying (and is thus guilty). However, this would also mean that Jim was telling the truth thus invalidating the requirement that there be only one true statement. So that scenario is out. And if Jim is telling the truth then Bud is lying (and is thus guilty). This would mean that Sam’s statement is true once again invalidating our one truth requirement. Thus Bud’s statement of innocence must be the true statement, meaning that Jim and Sam lied. Thus Jim is the guilty one.



  74. Steven Miller on October 17, 2011 at 1:14 am

    Glad you’re enjoing it.



  75. FF on October 16, 2011 at 6:46 am

    Very thoroughly researched, impressive work.



  76. Steven Miller on October 15, 2011 at 4:13 am

    this is one soln — could there be another?



  77. Linh on October 15, 2011 at 4:11 am

    Jim robbed the bank. Bud and Sam’s statements contradict one another so 1 gotta be true and the other is false. Assume Sam is truthful -> Bud and Jim are lying cos there’s only 1 truth -> both Bud and Jim robbed the bank (didnt say there can only be 1 person who robbed the bank. The problem only said that 1 was SUSPECTED).

    If Bud was truthful then Sam lied and Jim lied so Jim robbed the bank.

    Either case, Jim robbed the bank.



  78. Steven Miller on October 2, 2011 at 11:02 am

    That’s one solution — is there another?



  79. Al on October 2, 2011 at 5:16 am

    Baud stole the bank, and Jim knew that he did steal the bank and did not inform, so became a partner in robbing the bank, so he is not innocent.



  80. Steven Miller on September 29, 2011 at 10:19 pm

    To: ANT: Yes, your solution is valid. (Email me sjm1 AT williams.edu if you have a soln, as I prefer not to post a full soln as it can spoil the fun for some people).



  81. Steven Miller on September 27, 2011 at 4:36 am

    To Jack (who just posted): correct!



  82. Steven Miller on September 4, 2011 at 2:12 am

    This is one solution. There is another interpretation leading to another solution!



  83. Mahesh on September 3, 2011 at 3:37 pm

    1st supposition:(Jim is true i.e. Bud and Sam are false).But,If Bud is false here,Sam turns out to be true or else if Sam is false here,Bud turns out to be true i.e.Both Bud and Sam can’t be false.So supposition fails.
    2nd supposition:(Sam is true i.e. Bud and Jim are false).Ya obviously,Bud is false here but as Bud is guilty,Jim turns out to be innocent(true) here.So it fails again.
    3rd supposition:(Bud is true i.e. Jim and Sam are false).Here,Sam turns out to be false and obviously Jim also must turns out to be false to satisfy main condition(only 1 speaks truth).So supposition must holds good.
    Jim is speaking false,he must have robbed the bank.Is it correct?



  84. Steven Miller on June 1, 2011 at 4:06 pm

    There is another interpretation….



  85. Habeeba on June 1, 2011 at 1:26 pm

    Sam robbed the bank ! cause hes telling the truth



  86. Steven Miller on May 27, 2011 at 2:06 am

    Is there only one way to interpret this problem?



  87. frank on May 26, 2011 at 7:31 pm

    This is not true because bill lied



  88. Steven Miller on April 19, 2011 at 4:57 pm

    This is one way to look at it — is there another?



  89. Greg on April 19, 2011 at 4:56 pm

    Jim robbed the bank. But Sam should also be hauled in for trying to frame an innocent man.



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