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p, q, r | 16 Sep 2009

Discussion in '$1 Daily Competition' started by shabbir, Sep 16, 2009.

  1. shabbir

    shabbir Administrator Staff Member

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    X is positive integer of the form pqpqpqrq, such that (X-1) is a perfect square;

    where p, q and r different digits from 0 to 9, with p being nonzero.

    Determine X
     
  2. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    Possible solutions ::

    45454565
    82828202

    :D
     
  3. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    Brute-force solution :

    Code:
    #include <stdio.h>
    #include <math.h>
    
    int main()
    {
        unsigned int p,q,r, Num, SNum;
        for(int p = 1; p < 10; ++p)
        {
            for(int q = 0; q < 10; ++q)
            {
                for(int r = 0; r < 10; ++r)
                {
                    // pqpqpqrq
                    Num = p*(10101000);
                    Num += q*(1010101);
                    Num += r*10;
    
                    Num -= 1;
    
                    SNum = floor(sqrt(Num));
    
                    if(SNum * SNum == Num) {printf("p=%d q=%d r=%d\nX=%d\nX-1=%d\nsqrt(X-1)=%d\n\n", p,q,r,Num+1,Num,SNum);}
                }
            }
        }
        return 0;
    }
    Output ::

    Code:
    p=4 q=5 r=6
    X=45454565
    X-1=45454564
    sqrt(X-1)=6742
    
    p=8 q=2 r=0
    X=82828202
    X-1=82828201
    sqrt(X-1)=9101
    
    Process returned 0 (0x0)   execution time : 0.031 s
     
  4. shabbir

    shabbir Administrator Staff Member

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    I knew not many would attempt on this one. Congrats SP
     
  5. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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