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Puzzle for 27 Jun 2009

Discussion in '$1 Daily Competition' started by shabbir, Jun 27, 2009.

  1. shabbir

    shabbir Administrator Staff Member

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    Get a smallest three digit prime number which has
    1. All prime digits
    2. Forms a prime number with its sum of first two digits.
    3. Forms a prime number with its sum of last two digits.
     
  2. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    I think the smallest one is 523.

    EDIT :: The reason is :
    We have only 4 prime digits : 2, 3, 5 and 7.
    We can have 4C2 = 6 different combinations, taking 2 at a time.
    Out of these 6, only 2 have prime sums. They are 2,3 and 2,5.
    So, the number will be 325 or 523 as 2 should be common to 3 and 5.
    So, obviously 523 is the answer. :)
     
    Last edited: Jun 27, 2009
  3. shabbir

    shabbir Administrator Staff Member

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    Correct and also I have a bit different logic.

    2 Needs to be at middle because adding two odd number would always be even and so unprime
    So now we have
    _2_
    Now we have 3 which can be at last place because
    2 and 5 would make the number unprime
    7 would make the sum unprime
    _23
    Now
    and 3, 5 at first place are the only option
    and so 323 is not a prime number.

    I added smallest just to add confusion but the solution is unique.
     
  4. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    I knew that :D
     

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