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Pick two numbers! (Posted on 2005-11-22) Difficulty: 4 of 5
Yesterday I bought two tickets to a movie, which logically had consecutive numbers. I examined the numbers, which had four digits, and mentioned that the sum of the eight digits was 25.

A friend asked if any digit appeared more than twice out of the eight, and I answered him.

Other friend asked if the sum of the digits of either ticket was equal to 13, which I also answered.

And then, to my surprise, my daughter told me what the two numbers were!

What were they?

  Submitted by e.g.    
Rating: 3.8889 (9 votes)
Solution: (Hide)
Suppose I answered that one of the tickets' digits summed 13. The tickets could have been numbered ABCD and ABC(D+1) with D<9 and you couldn't work out the numbers, since all you'd have is that A+B+C+D=12. So I answered "NO" to the second question, and the numbers aren't ABCD and ABC(D+1).

If the tickets had been numbered ABC9 and AB(C+1)0, with C<9, then the sum of the digits would have been even, so this case is impossible.

Finally, as the numbers cannot be A999 and (A+1)000 --for the sum exceeds 25-- the tickets must have been AB99 and A(B+1)00, so A+B=3, allowing 0399-0400, 1299-1300, 2199-2200, and 3099-3100. In three of these I would have answered "YES" to the question about a number appearing more than twice; since my daughter could work out the numbers, I must have answered "NO" and the tickets were 1299-1300.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2008-11-16 14:11:30
ticket triviacassie2006-01-05 08:32:35
No SubjectJames2005-11-25 15:53:23
Answer to the Two Ticket ProblemGordon Steel2005-11-24 16:58:55
*sizzle*FastJazzy2005-11-23 22:52:43
Solutionmy answerScott2005-11-23 04:11:14
re: I disagreeJames2005-11-23 00:32:18
re: I disagreeMindy Rodriguez2005-11-23 00:31:38
Some ThoughtsI disagreeJames2005-11-23 00:25:25
Some Thoughtsre: solnMindy Rodriguez2005-11-22 22:55:36
Solutionmy answerVernon Lewis2005-11-22 12:46:55
SolutionSolutionNeil2005-11-22 12:42:14
SolutionRoscoe2005-11-22 12:18:04
SolutionMy solutionpcbouhid2005-11-22 11:48:19
solndoubledos2005-11-22 11:00:52
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