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Puzzle for 25 Jun 2009

Discussion in '$1 Daily Competition' started by shabbir, Jun 25, 2009.

  1. shabbir

    shabbir Administrator Staff Member

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    Find a three digit prime number which

    • Has all prime digits
    • Forms primes with its first two digits.
    • Forms primes with its last two digits.
     
  2. nimesh

    nimesh New Member

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    I say 373

    Has all prime digits - All are Prime 3, 7
    Forms primes with its first two digits - Forms Prime with first 2 digits 37
    Forms primes with its and last two digits. - Forms Prime with Last two - 73

    The last condition looks incomplete.
    There was no condition of uniqueness of digits
    There was no condition like least 3 digit prime :)
     
  3. Mridula

    Mridula New Member

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    179 - 3 unique digit prime no.

    17 is a prime no.
    79 is prime no.
     
  4. nimesh

    nimesh New Member

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    But 1 is not a prime no :lol:
    Sorry Mridula for Yesterday
     
  5. shabbir

    shabbir Administrator Staff Member

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    Like.
    Dont confuse with yesterdays problem and its a fresh one with not any condition.

    I would like to also see a reason as to how you landed to the number you have as answer.
     
  6. nimesh

    nimesh New Member

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    "The last condition looks incomplete."
    I mean the sentence formation is incorrect. Which you have corrected now...haha

    What reason would you like? [btw, you didn't asked earlier to specify the reason]
    I just looked at the list of prime numbers and checked with the conditions you gave.

    Other numbers that I thought were:
    113, 131, 137, 173, 197, 311, 313, 317 - But 1 is not a prime number
    So the first number that I got was 373
     
  7. xpi0t0s

    xpi0t0s Mentor

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    All possible results are
    237
    373
    537
    737

    Code:
    int is_prime(int n)
    {
    	if (n==2) return 1;
    	if (n<3) return 0;
    	if (!(n%2)) return 0;
    	for (int i=3; i*i<=n; i+=2)
    	{
    		if (!(n%i))
    			return 0;
    	}
    	return 1;
    }
    
    int _tmain(int argc, _TCHAR* argv[])
    {
    	for (int i=100; i<1000; i++)
    	{
    		int digits[3];
    		int temp=i;
    		digits[2]=temp%10; temp/=10;
    		digits[1]=temp%10; temp/=10;
    		digits[0]=temp%10;
    		temp=i;
    		int ms100,ls100;
    		ms100=digits[0]*10+digits[1];
    		ls100=digits[1]*10+digits[2];
    		if (is_prime(digits[0]) && is_prime(digits[1]) && is_prime(digits[2]))
    		{
    			if (is_prime(ms100) && is_prime(ls100))
    			{
    				printf("%d\n",i);
    			}
    		}
    	}
    	return 0;
    }
    
     
  8. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    LOL @ xpi0t0s, you brute-forced the solution for such a simple question !!
    I mean, shabbir didn't even mention the word "smallest". So, that was really easy to figure out a 3-digit number.

    Congrats nimesh.

    @ shabbir:
    So, you changed the posting time today (by almost -12 hours) !! :(
    I'll have to wait till 2morrow.
     
    Last edited: Jun 25, 2009
  9. nimesh

    nimesh New Member

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    xpi0t0s - 237 is not a prime number (237 = 3 * 79) List of Prime Numbers

    Thanks Saswat, but the winner is not yet confirmed by Shabbir :)
     
  10. xpi0t0s

    xpi0t0s Mentor

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    Whoops, you're right, neither are 537 and 737 so the only result is 373. Adding
    Code:
    if (is_prime(i))
    
    fixed the problem.
     
  11. xpi0t0s

    xpi0t0s Mentor

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    Yes Saswat I brute forced it. I'm obviously not up to your standards.
     
  12. shabbir

    shabbir Administrator Staff Member

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    Yes. It was not conditional error but a typo.

    Just curious. Nothing to with the competition

    So its not predictable. :D

    Logic is also there. 2,3,5,7 are the digits which needs to be filled in the 3 slots.

    • 2 and 5 cannot come in the last slot other wise number would not be prime, so it has to be 3 and 7.
    • With the above logic 2 and 5 also cannot come in the second slot as the number with those should also be prime.
    • Any combination of 5,3,7 or 2,3,7 is divisible by 3
    • 7 and 3 cannot be at consecutive places as we need primes by both the numbers.
    • so the option left is 373 and 737
    • 737 is not prime
    Winner is Nimesh and I did not mention smallest largest anything because I knew it has unique solution
     
    nimesh likes this.
  13. nimesh

    nimesh New Member

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    Cool...
    Nice explanation Shabbir. I like it.:2thumbsup
     
  14. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    So, you have implemented a manual version of my random posting time idea :D
     
  15. shabbir

    shabbir Administrator Staff Member

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    To an extent.
     

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