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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;
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
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!
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Project Euler #136: Singleton difference
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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;
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
My solution for the sample test is:
Can anybody confirm that? Thanks!