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-   $1 Daily Competition (http://www.go4expert.com/contests/daily-competition/)
-   -   Puzzle for 25 Jun 2009 (http://www.go4expert.com/contests/puzzle-for-25-jun-2009-t18178/)

shabbir 25Jun2009 09:43

Puzzle for 25 Jun 2009
 
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.

nimesh 25Jun2009 10:35

Re: Puzzle for 25 Jun 2009
 
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 :)

Mridula 25Jun2009 10:50

Re: Puzzle for 25 Jun 2009
 
179 - 3 unique digit prime no.

17 is a prime no.
79 is prime no.

nimesh 25Jun2009 10:52

Re: Puzzle for 25 Jun 2009
 
Quote:

Originally Posted by Mridula (Post 50441)
179 - 3 unique digit prime no.

17 is a prime no.
79 is prime no.

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

shabbir 25Jun2009 11:01

Re: Puzzle for 25 Jun 2009
 
Quote:

Originally Posted by nimesh (Post 50440)
The last condition looks incomplete.

Like.
Quote:

Originally Posted by nimesh (Post 50440)
There was no condition of uniqueness of digits
There was no condition like least 3 digit prime :)

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.

nimesh 25Jun2009 11:27

Re: Puzzle for 25 Jun 2009
 
"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

xpi0t0s 25Jun2009 12:44

Re: Puzzle for 25 Jun 2009
 
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;
}


SaswatPadhi 25Jun2009 13:08

Re: Puzzle for 25 Jun 2009
 
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.

nimesh 25Jun2009 14:07

Re: Puzzle for 25 Jun 2009
 
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 :)

xpi0t0s 25Jun2009 14:27

Re: Puzzle for 25 Jun 2009
 
Whoops, you're right, neither are 537 and 737 so the only result is 373. Adding
Code:

if (is_prime(i))
fixed the problem.


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