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Bus ticket and sum of digits puzzle

  1. Dec 3, 2009 #1
    Yesterday Professor Q rode on a bus with his friend. As soon as he got the tickets for himself and his friend, which were consecutively numbered with each of the tickets bearing a 5-digit number with no leading zero, he added the digits on them and told his friend that the sum of all ten digits was exactly 62.

    His logical friend asked him if the sum of the numbers on either of the tickets was by any chance 35. Professor Q answered his friend, whereby his friend immediately deduced the numbers on the bus tickets.

    What were the numbers on the two bus tickets?
     
  2. jcsd
  3. Dec 3, 2009 #2
    56789
    56790

    I know that if the answer to the question is yes, then the last digit has to be a 9 and the four other digits have to add up to 26, is there any other logic than that?
     
    Last edited: Dec 3, 2009
  4. Dec 3, 2009 #3
    f(x) wouldn't say 46799 fulfill what is required (for the first ticket as well)... I got the same numbers as you my first try but I assumed numbers don't repeat on individual tickets... but it doesn't say that in the riddle.
     
  5. Dec 3, 2009 #4
    But does it add up to 62?
     
  6. Dec 4, 2009 #5
    Well you need a second ticket.... 46799 + 56790 orrr 46790 + 37890 is this wrong and I am crazy or does the first number make 35 and the sum of all 10 makes 62...?
    How about
    56789 + 37890??????

    There are so man possible combinations... even that second one none of the numbers repeat on the same ticket but the answer still varies from what you gave...
     
  7. Dec 4, 2009 #6
    But they have to be consecutive digits :wink:
     
  8. Dec 4, 2009 #7
    WOW HAHAHA. When I first did it I realized that but when I looked at it AGAIN I guess I forgot. I'm so dumb :tongue:
     
  9. Dec 5, 2009 #8

    Borek

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    Staff: Mentor

    If sum of digits of either number is 35, there are many possible answers, but if neither is 35 - there is only one.

    98999 & 99000
     
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