Project Euler #136: Singleton difference

  • + 1 comment

    Please find my unique solution. Requesting comment on this context for all.

    1) (3*3)-(2*2)-(1*1)=4 ;
    2) (8*8)-(6*6)-(4*4)=12;
    3) (5*5)-(3*3)-(1*1)=15;
    4) (6*6)-(4*4)-(2*2)=16;
    5) (13*13)-(10*10)-(7*7)=20;
    6) (12*12)-(9*9)-(6*6)=27;
    7) (18*18)-(14*14)-(10*10)=28;
    8) (7*7)-(4*4)-(1*1)=32;
    9) (8*8)-(5*5)-(2*2)=35;
    10) (9*9)-(6*6)-(3*3)=36;
    11) (17*17)-(13*13)-(9*9)=39;
    12) (28*28)-(22*22)-(16*16)=44;
    13) (16*16)-(12*12)-(8*8)=48;
    14) (22*22)-(17*17)-(12*12)=51;
    15) (33*33)-(26*26)-(19*19)=52;
    16) (9*9)-(5*5)-(1*1)=55;
    17) (10*10)-(6*6)-(2*2)=60;
    18) (11*11)-(7*7)-(3*3)=63;
    19) (12*12)-(8*8)-(4*4)=64;
    20) (43*43)-(34*34)-(25*25)=68;
    21) (20*20)-(15*15)-(10*10)=75;
    22) (48*48)-(38*38)-(28*28)=76;
    23) (26*26)-(20*20)-(14*14)=80;
    24) (11*11)-(6*6)-(1*1)=84;
    25) (37*37)-(29*29)-(21*21)=87;
    26) (12*12)-(7*7)-(2*2)=91;
    27) (58*58)-(46*46)-(34*34)=92;
    28) (25*25)-(19*19)-(13*13)=95;
    29) (13*13)-(8*8)-(3*3)=96;
    30) (14*14)-(9*9)-(4*4)=99;

    • + 1 comment

      I only checked your numbers up to 18).

      Yours results for 15, 27, 32, 35, 36, 51, 55, 60, 63 are not unique.

      5^2 - 3^2 - 1^2 = 15 7^2 - 5^2 - 3^2 = 15 19^2 - 15^2 - 11^2 = 15

      12^2 - 9^2 - 6^2 = 27 34^2 - 27^2 - 20^2 = 27

      7^2 - 4^2 - 1^2 = 32 11^2 - 8^2 - 5^2 = 32

      8^2 - 5^2 - 2^2 = 35 10^2 - 7^2 - 4^2 = 35 44^2 - 35^2 - 26^2 = 35

      9^2 - 6^2 - 3^2 = 36 23^2 - 18^2 - 13^2 = 36

      22^2 - 17^2 - 12^2 = 51 64^2 - 51^2 - 38^2 = 51

      9^2 - 5^2 - 1^2 = 55 15^2 - 11^2 - 7^2 = 55 69^2 - 55^2 - 41^2 = 55

      10^2 - 6^2 - 2^2 = 60 14^2 - 10^2 - 6^2 = 60 38^2 - 30^2 - 22^2 = 60

      11^2 - 7^2 - 3^2 = 63 13^2 - 9^2 - 5^2 = 63 27^2 - 21^2 - 15^2 = 63 79^2 - 63^2 - 47^2 = 63

      • + 0 comments

        My solution for the sample test is:

         1  4^2 - 3^2 - 2^2 = 3
         2  3^2 - 2^2 - 1^2 = 4
         3  9^2 - 7^2 - 5^2 = 7
         4  14^2 - 11^2 - 8^2 = 11
         5  8^2 - 6^2 - 4^2 = 12
         6  6^2 - 4^2 - 2^2 = 16
         7  24^2 - 19^2 - 14^2 = 19
         8  13^2 - 10^2 - 7^2 = 20
         9  29^2 - 23^2 - 17^2 = 23
        10  18^2 - 14^2 - 10^2 = 28
        11  39^2 - 31^2 - 23^2 = 31
        12  54^2 - 43^2 - 32^2 = 43
        13  28^2 - 22^2 - 16^2 = 44
        14  59^2 - 47^2 - 35^2 = 47
        15  16^2 - 12^2 - 8^2 = 48
        16  33^2 - 26^2 - 19^2 = 52
        17  74^2 - 59^2 - 44^2 = 59
        18  84^2 - 67^2 - 50^2 = 67
        19  43^2 - 34^2 - 25^2 = 68
        20  89^2 - 71^2 - 53^2 = 71
        21  48^2 - 38^2 - 28^2 = 76
        22  99^2 - 79^2 - 59^2 = 79
        23  26^2 - 20^2 - 14^2 = 80
        24  104^2 - 83^2 - 62^2 = 83
        25  58^2 - 46^2 - 34^2 = 92
        

        Can anybody confirm that? Thanks!