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@robinhouston
Created September 17, 2020 14:28
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3×3 troll-square matrices with two-digit entries
sage: %paste
def cgfh(cg_plus_fh):
for cg in range(1, cg_plus_fh):
fh = cg_plus_fh - cg
for c in divisors(cg):
for f in divisors(fh):
yield (c, cg//c, f, fh//f)
for r in range(1, 99, 2):
cg_plus_fh = (101^2 - r^2)/4
for (c, g, f, h) in cgfh(cg_plus_fh):
a = (101*c*g + c*g*r) / (2 * cg_plus_fh)
b = (c*h*(r + 101)) / (2 * cg_plus_fh)
d = (f*g*(r + 101)) / (2 * cg_plus_fh)
e = (f*h*(r + 101)) / (2 * cg_plus_fh)
i = (101 - r) / 2
if (
frac(a) == 0 and frac(b) == 0 and frac(d) == 0 and frac(e) == 0
and 10 <= a < 100 and 10 <= b < 100 and 10 <= c < 100
and 10 <= d < 100 and 10 <= e < 100 and 10 <= f < 100
and 10 <= g < 100 and 10 <= h < 100 and 10 <= i < 100
):
print("{{%d, %d, %d}, {%d, %d, %d}, {%d, %d, %d}}" % (a,b,c,d,e,f,g,h,i))
## -- End pasted text --
{{10, 10, 10}, {41, 41, 41}, {50, 50, 50}}
{{10, 10, 20}, {41, 41, 82}, {25, 25, 50}}
{{10, 41, 25}, {10, 41, 25}, {20, 82, 50}}
{{10, 41, 50}, {10, 41, 50}, {10, 41, 50}}
{{11, 10, 10}, {44, 40, 40}, {55, 50, 50}}
{{11, 11, 11}, {40, 40, 40}, {50, 50, 50}}
{{11, 22, 22}, {20, 40, 40}, {25, 50, 50}}
{{11, 11, 22}, {40, 40, 80}, {25, 25, 50}}
{{11, 40, 25}, {11, 40, 25}, {22, 80, 50}}
{{11, 20, 25}, {22, 40, 50}, {22, 40, 50}}
{{11, 40, 50}, {11, 40, 50}, {11, 40, 50}}
{{11, 44, 55}, {10, 40, 50}, {10, 40, 50}}
{{12, 13, 10}, {36, 39, 30}, {60, 65, 50}}
{{12, 18, 12}, {26, 39, 26}, {50, 75, 50}}
{{12, 12, 12}, {39, 39, 39}, {50, 50, 50}}
{{12, 26, 20}, {18, 39, 30}, {30, 65, 50}}
{{12, 12, 20}, {39, 39, 65}, {30, 30, 50}}
{{12, 36, 24}, {13, 39, 26}, {25, 75, 50}}
{{12, 12, 24}, {39, 39, 78}, {25, 25, 50}}
{{12, 39, 25}, {12, 39, 25}, {24, 78, 50}}
{{12, 13, 25}, {36, 39, 75}, {24, 26, 50}}
{{12, 39, 30}, {12, 39, 30}, {20, 65, 50}}
{{12, 18, 30}, {26, 39, 65}, {20, 30, 50}}
{{12, 39, 50}, {12, 39, 50}, {12, 39, 50}}
{{12, 26, 50}, {18, 39, 75}, {12, 26, 50}}
{{12, 36, 60}, {13, 39, 65}, {10, 30, 50}}
{{13, 19, 10}, {26, 38, 20}, {65, 95, 50}}
{{13, 13, 13}, {38, 38, 38}, {50, 50, 50}}
{{13, 38, 25}, {13, 38, 25}, {26, 76, 50}}
{{13, 19, 25}, {26, 38, 50}, {26, 38, 50}}
{{13, 26, 26}, {19, 38, 38}, {25, 50, 50}}
{{13, 13, 26}, {38, 38, 76}, {25, 25, 50}}
{{13, 38, 50}, {13, 38, 50}, {13, 38, 50}}
{{13, 26, 65}, {19, 38, 95}, {10, 20, 50}}
{{14, 14, 14}, {37, 37, 37}, {50, 50, 50}}
{{14, 37, 25}, {14, 37, 25}, {28, 74, 50}}
{{14, 14, 28}, {37, 37, 74}, {25, 25, 50}}
{{14, 37, 50}, {14, 37, 50}, {14, 37, 50}}
{{15, 18, 10}, {30, 36, 20}, {75, 90, 50}}
{{15, 15, 10}, {36, 36, 24}, {75, 75, 50}}
{{15, 12, 10}, {45, 36, 30}, {75, 60, 50}}
{{15, 10, 10}, {54, 36, 36}, {75, 50, 50}}
{{15, 27, 15}, {20, 36, 20}, {50, 90, 50}}
{{15, 18, 15}, {30, 36, 30}, {50, 60, 50}}
{{15, 15, 15}, {36, 36, 36}, {50, 50, 50}}
{{15, 12, 15}, {45, 36, 45}, {50, 40, 50}}
{{15, 45, 25}, {12, 36, 20}, {30, 90, 50}}
{{15, 36, 25}, {15, 36, 25}, {30, 72, 50}}
{{15, 30, 25}, {18, 36, 30}, {30, 60, 50}}
{{15, 20, 25}, {27, 36, 45}, {30, 40, 50}}
{{15, 18, 25}, {30, 36, 50}, {30, 36, 50}}
{{15, 15, 25}, {36, 36, 60}, {30, 30, 50}}
{{15, 12, 25}, {45, 36, 75}, {30, 24, 50}}
{{15, 10, 25}, {54, 36, 90}, {30, 20, 50}}
{{15, 54, 30}, {10, 36, 20}, {25, 90, 50}}
{{15, 45, 30}, {12, 36, 24}, {25, 75, 50}}
{{15, 36, 30}, {15, 36, 30}, {25, 60, 50}}
{{15, 30, 30}, {18, 36, 36}, {25, 50, 50}}
{{15, 27, 30}, {20, 36, 40}, {25, 45, 50}}
{{15, 18, 30}, {30, 36, 60}, {25, 30, 50}}
{{15, 15, 30}, {36, 36, 72}, {25, 25, 50}}
{{15, 12, 30}, {45, 36, 90}, {25, 20, 50}}
{{15, 45, 50}, {12, 36, 40}, {15, 45, 50}}
{{15, 36, 50}, {15, 36, 50}, {15, 36, 50}}
{{15, 30, 50}, {18, 36, 60}, {15, 30, 50}}
{{15, 20, 50}, {27, 36, 90}, {15, 20, 50}}
{{15, 54, 75}, {10, 36, 50}, {10, 36, 50}}
{{15, 45, 75}, {12, 36, 60}, {10, 30, 50}}
{{15, 36, 75}, {15, 36, 75}, {10, 24, 50}}
{{15, 30, 75}, {18, 36, 90}, {10, 20, 50}}
{{16, 14, 10}, {40, 35, 25}, {80, 70, 50}}
{{16, 10, 10}, {56, 35, 35}, {80, 50, 50}}
{{16, 16, 16}, {35, 35, 35}, {50, 50, 50}}
{{16, 28, 20}, {20, 35, 25}, {40, 70, 50}}
{{16, 20, 20}, {28, 35, 35}, {40, 50, 50}}
{{16, 14, 20}, {40, 35, 50}, {40, 35, 50}}
{{16, 10, 20}, {56, 35, 70}, {40, 25, 50}}
{{16, 35, 25}, {16, 35, 25}, {32, 70, 50}}
{{16, 16, 32}, {35, 35, 70}, {25, 25, 50}}
{{16, 56, 40}, {10, 35, 25}, {20, 70, 50}}
{{16, 40, 40}, {14, 35, 35}, {20, 50, 50}}
{{16, 28, 40}, {20, 35, 50}, {20, 35, 50}}
{{16, 20, 40}, {28, 35, 70}, {20, 25, 50}}
{{16, 35, 50}, {16, 35, 50}, {16, 35, 50}}
{{16, 56, 80}, {10, 35, 50}, {10, 35, 50}}
{{16, 40, 80}, {14, 35, 70}, {10, 25, 50}}
{{17, 17, 10}, {34, 34, 20}, {85, 85, 50}}
{{17, 17, 17}, {34, 34, 34}, {50, 50, 50}}
{{17, 34, 25}, {17, 34, 25}, {34, 68, 50}}
{{17, 17, 25}, {34, 34, 50}, {34, 34, 50}}
{{17, 34, 34}, {17, 34, 34}, {25, 50, 50}}
{{17, 17, 34}, {34, 34, 68}, {25, 25, 50}}
{{17, 34, 50}, {17, 34, 50}, {17, 34, 50}}
{{17, 34, 85}, {17, 34, 85}, {10, 20, 50}}
{{18, 11, 10}, {54, 33, 30}, {90, 55, 50}}
{{18, 18, 12}, {33, 33, 22}, {75, 75, 50}}
{{18, 27, 18}, {22, 33, 22}, {50, 75, 50}}
{{18, 18, 18}, {33, 33, 33}, {50, 50, 50}}
{{18, 22, 20}, {27, 33, 30}, {45, 55, 50}}
{{18, 33, 25}, {18, 33, 25}, {36, 66, 50}}
{{18, 11, 25}, {54, 33, 75}, {36, 22, 50}}
{{18, 33, 30}, {18, 33, 30}, {30, 55, 50}}
{{18, 18, 30}, {33, 33, 55}, {30, 30, 50}}
{{18, 54, 36}, {11, 33, 22}, {25, 75, 50}}
{{18, 18, 36}, {33, 33, 66}, {25, 25, 50}}
{{18, 27, 45}, {22, 33, 55}, {20, 30, 50}}
{{18, 33, 50}, {18, 33, 50}, {18, 33, 50}}
{{18, 22, 50}, {27, 33, 75}, {18, 22, 50}}
{{18, 33, 75}, {18, 33, 75}, {12, 22, 50}}
{{18, 54, 90}, {11, 33, 55}, {10, 30, 50}}
{{19, 16, 10}, {38, 32, 20}, {95, 80, 50}}
{{19, 19, 19}, {32, 32, 32}, {50, 50, 50}}
{{19, 32, 25}, {19, 32, 25}, {38, 64, 50}}
{{19, 16, 25}, {38, 32, 50}, {38, 32, 50}}
{{19, 38, 38}, {16, 32, 32}, {25, 50, 50}}
{{19, 19, 38}, {32, 32, 64}, {25, 25, 50}}
{{19, 32, 50}, {19, 32, 50}, {19, 32, 50}}
{{19, 38, 95}, {16, 32, 80}, {10, 20, 50}}
{{20, 20, 20}, {31, 31, 31}, {50, 50, 50}}
{{20, 10, 20}, {62, 31, 62}, {50, 25, 50}}
{{20, 31, 25}, {20, 31, 25}, {40, 62, 50}}
{{20, 20, 40}, {31, 31, 62}, {25, 25, 50}}
{{20, 62, 50}, {10, 31, 25}, {20, 62, 50}}
{{20, 31, 50}, {20, 31, 50}, {20, 31, 50}}
{{21, 21, 14}, {30, 30, 20}, {75, 75, 50}}
{{21, 14, 14}, {45, 30, 30}, {75, 50, 50}}
{{21, 18, 15}, {35, 30, 25}, {70, 60, 50}}
{{21, 15, 15}, {42, 30, 30}, {70, 50, 50}}
{{21, 21, 21}, {30, 30, 30}, {50, 50, 50}}
{{21, 30, 25}, {21, 30, 25}, {42, 60, 50}}
{{21, 15, 25}, {42, 30, 50}, {42, 30, 50}}
{{21, 10, 25}, {63, 30, 75}, {42, 20, 50}}
{{21, 45, 30}, {14, 30, 20}, {35, 75, 50}}
{{21, 30, 30}, {21, 30, 30}, {35, 50, 50}}
{{21, 18, 30}, {35, 30, 50}, {35, 30, 50}}
{{21, 15, 30}, {42, 30, 60}, {35, 25, 50}}
{{21, 42, 35}, {15, 30, 25}, {30, 60, 50}}
{{21, 35, 35}, {18, 30, 30}, {30, 50, 50}}
{{21, 21, 35}, {30, 30, 50}, {30, 30, 50}}
{{21, 14, 35}, {45, 30, 75}, {30, 20, 50}}
{{21, 63, 42}, {10, 30, 20}, {25, 75, 50}}
{{21, 42, 42}, {15, 30, 30}, {25, 50, 50}}
{{21, 21, 42}, {30, 30, 60}, {25, 25, 50}}
{{21, 30, 50}, {21, 30, 50}, {21, 30, 50}}
{{21, 42, 70}, {15, 30, 50}, {15, 30, 50}}
{{21, 35, 70}, {18, 30, 60}, {15, 25, 50}}
{{21, 45, 75}, {14, 30, 50}, {14, 30, 50}}
{{21, 30, 75}, {21, 30, 75}, {14, 20, 50}}
{{22, 22, 22}, {29, 29, 29}, {50, 50, 50}}
{{22, 11, 22}, {58, 29, 58}, {50, 25, 50}}
{{22, 29, 25}, {22, 29, 25}, {44, 58, 50}}
{{22, 22, 44}, {29, 29, 58}, {25, 25, 50}}
{{22, 58, 50}, {11, 29, 25}, {22, 58, 50}}
{{22, 29, 50}, {22, 29, 50}, {22, 29, 50}}
{{23, 23, 23}, {28, 28, 28}, {50, 50, 50}}
{{23, 28, 25}, {23, 28, 25}, {46, 56, 50}}
{{23, 14, 25}, {46, 28, 50}, {46, 28, 50}}
{{23, 46, 46}, {14, 28, 28}, {25, 50, 50}}
{{23, 23, 46}, {28, 28, 56}, {25, 25, 50}}
{{23, 28, 50}, {23, 28, 50}, {23, 28, 50}}
{{24, 27, 15}, {24, 27, 15}, {80, 90, 50}}
{{24, 24, 16}, {27, 27, 18}, {75, 75, 50}}
{{24, 36, 20}, {18, 27, 15}, {60, 90, 50}}
{{24, 18, 20}, {36, 27, 30}, {60, 45, 50}}
{{24, 12, 20}, {54, 27, 45}, {60, 30, 50}}
{{24, 36, 24}, {18, 27, 18}, {50, 75, 50}}
{{24, 24, 24}, {27, 27, 27}, {50, 50, 50}}
{{24, 12, 24}, {54, 27, 54}, {50, 25, 50}}
{{24, 27, 25}, {24, 27, 25}, {48, 54, 50}}
{{24, 54, 30}, {12, 27, 15}, {40, 90, 50}}
{{24, 27, 30}, {24, 27, 30}, {40, 45, 50}}
{{24, 18, 30}, {36, 27, 45}, {40, 30, 50}}
{{24, 36, 40}, {18, 27, 30}, {30, 45, 50}}
{{24, 24, 40}, {27, 27, 45}, {30, 30, 50}}
{{24, 12, 40}, {54, 27, 90}, {30, 15, 50}}
{{24, 24, 48}, {27, 27, 54}, {25, 25, 50}}
{{24, 54, 50}, {12, 27, 25}, {24, 54, 50}}
{{24, 27, 50}, {24, 27, 50}, {24, 27, 50}}
{{24, 18, 50}, {36, 27, 75}, {24, 18, 50}}
{{24, 54, 60}, {12, 27, 30}, {20, 45, 50}}
{{24, 36, 60}, {18, 27, 45}, {20, 30, 50}}
{{24, 18, 60}, {36, 27, 90}, {20, 15, 50}}
{{24, 27, 75}, {24, 27, 75}, {16, 18, 50}}
{{24, 24, 80}, {27, 27, 90}, {15, 15, 50}}
{{25, 26, 25}, {25, 26, 25}, {50, 52, 50}}
{{25, 25, 25}, {26, 26, 26}, {50, 50, 50}}
{{25, 13, 25}, {50, 26, 50}, {50, 26, 50}}
{{25, 10, 25}, {65, 26, 65}, {50, 20, 50}}
{{25, 65, 50}, {10, 26, 20}, {25, 65, 50}}
{{25, 50, 50}, {13, 26, 26}, {25, 50, 50}}
{{25, 26, 50}, {25, 26, 50}, {25, 26, 50}}
{{25, 25, 50}, {26, 26, 52}, {25, 25, 50}}
{{26, 10, 20}, {65, 25, 50}, {65, 25, 50}}
{{26, 25, 25}, {26, 25, 25}, {52, 50, 50}}
{{26, 26, 26}, {25, 25, 25}, {50, 50, 50}}
{{26, 13, 26}, {50, 25, 50}, {50, 25, 50}}
{{26, 50, 50}, {13, 25, 25}, {26, 50, 50}}
{{26, 25, 50}, {26, 25, 50}, {26, 25, 50}}
{{26, 26, 52}, {25, 25, 50}, {25, 25, 50}}
{{26, 65, 65}, {10, 25, 25}, {20, 50, 50}}
{{27, 24, 15}, {27, 24, 15}, {90, 80, 50}}
{{27, 18, 15}, {36, 24, 20}, {90, 60, 50}}
{{27, 12, 15}, {54, 24, 30}, {90, 40, 50}}
{{27, 27, 18}, {24, 24, 16}, {75, 75, 50}}
{{27, 18, 18}, {36, 24, 24}, {75, 50, 50}}
{{27, 24, 25}, {27, 24, 25}, {54, 48, 50}}
{{27, 12, 25}, {54, 24, 50}, {54, 24, 50}}
{{27, 27, 27}, {24, 24, 24}, {50, 50, 50}}
{{27, 36, 30}, {18, 24, 20}, {45, 60, 50}}
{{27, 24, 30}, {27, 24, 30}, {45, 40, 50}}
{{27, 18, 30}, {36, 24, 40}, {45, 30, 50}}
{{27, 12, 30}, {54, 24, 60}, {45, 20, 50}}
{{27, 54, 45}, {12, 24, 20}, {30, 60, 50}}
{{27, 36, 45}, {18, 24, 30}, {30, 40, 50}}
{{27, 27, 45}, {24, 24, 40}, {30, 30, 50}}
{{27, 18, 45}, {36, 24, 60}, {30, 20, 50}}
{{27, 24, 50}, {27, 24, 50}, {27, 24, 50}}
{{27, 54, 54}, {12, 24, 24}, {25, 50, 50}}
{{27, 27, 54}, {24, 24, 48}, {25, 25, 50}}
{{27, 36, 75}, {18, 24, 50}, {18, 24, 50}}
{{27, 24, 75}, {27, 24, 75}, {18, 16, 50}}
{{27, 54, 90}, {12, 24, 40}, {15, 30, 50}}
{{27, 36, 90}, {18, 24, 60}, {15, 20, 50}}
{{27, 27, 90}, {24, 24, 80}, {15, 15, 50}}
{{28, 23, 25}, {28, 23, 25}, {56, 46, 50}}
{{28, 28, 28}, {23, 23, 23}, {50, 50, 50}}
{{28, 14, 28}, {46, 23, 46}, {50, 25, 50}}
{{28, 46, 50}, {14, 23, 25}, {28, 46, 50}}
{{28, 23, 50}, {28, 23, 50}, {28, 23, 50}}
{{28, 28, 56}, {23, 23, 46}, {25, 25, 50}}
{{29, 22, 25}, {29, 22, 25}, {58, 44, 50}}
{{29, 11, 25}, {58, 22, 50}, {58, 22, 50}}
{{29, 29, 29}, {22, 22, 22}, {50, 50, 50}}
{{29, 22, 50}, {29, 22, 50}, {29, 22, 50}}
{{29, 58, 58}, {11, 22, 22}, {25, 50, 50}}
{{29, 29, 58}, {22, 22, 44}, {25, 25, 50}}
{{30, 30, 20}, {21, 21, 14}, {75, 75, 50}}
{{30, 14, 20}, {45, 21, 30}, {75, 35, 50}}
{{30, 10, 20}, {63, 21, 42}, {75, 25, 50}}
{{30, 35, 25}, {18, 21, 15}, {60, 70, 50}}
{{30, 21, 25}, {30, 21, 25}, {60, 42, 50}}
{{30, 15, 25}, {42, 21, 35}, {60, 30, 50}}
{{30, 45, 30}, {14, 21, 14}, {50, 75, 50}}
{{30, 42, 30}, {15, 21, 15}, {50, 70, 50}}
{{30, 30, 30}, {21, 21, 21}, {50, 50, 50}}
{{30, 21, 30}, {30, 21, 30}, {50, 35, 50}}
{{30, 18, 30}, {35, 21, 35}, {50, 30, 50}}
{{30, 15, 30}, {42, 21, 42}, {50, 25, 50}}
{{30, 42, 50}, {15, 21, 25}, {30, 42, 50}}
{{30, 35, 50}, {18, 21, 30}, {30, 35, 50}}
{{30, 30, 50}, {21, 21, 35}, {30, 30, 50}}
{{30, 21, 50}, {30, 21, 50}, {30, 21, 50}}
{{30, 15, 50}, {42, 21, 70}, {30, 15, 50}}
{{30, 14, 50}, {45, 21, 75}, {30, 14, 50}}
{{30, 42, 60}, {15, 21, 30}, {25, 35, 50}}
{{30, 30, 60}, {21, 21, 42}, {25, 25, 50}}
{{30, 18, 60}, {35, 21, 70}, {25, 15, 50}}
{{30, 63, 75}, {10, 21, 25}, {20, 42, 50}}
{{30, 45, 75}, {14, 21, 35}, {20, 30, 50}}
{{30, 21, 75}, {30, 21, 75}, {20, 14, 50}}
{{31, 20, 25}, {31, 20, 25}, {62, 40, 50}}
{{31, 10, 25}, {62, 20, 50}, {62, 20, 50}}
{{31, 31, 31}, {20, 20, 20}, {50, 50, 50}}
{{31, 20, 50}, {31, 20, 50}, {31, 20, 50}}
{{31, 62, 62}, {10, 20, 20}, {25, 50, 50}}
{{31, 31, 62}, {20, 20, 40}, {25, 25, 50}}
{{32, 38, 20}, {16, 19, 10}, {80, 95, 50}}
{{32, 19, 25}, {32, 19, 25}, {64, 38, 50}}
{{32, 32, 32}, {19, 19, 19}, {50, 50, 50}}
{{32, 16, 32}, {38, 19, 38}, {50, 25, 50}}
{{32, 38, 50}, {16, 19, 25}, {32, 38, 50}}
{{32, 19, 50}, {32, 19, 50}, {32, 19, 50}}
{{32, 32, 64}, {19, 19, 38}, {25, 25, 50}}
{{32, 16, 80}, {38, 19, 95}, {20, 10, 50}}
{{33, 33, 22}, {18, 18, 12}, {75, 75, 50}}
{{33, 22, 22}, {27, 18, 18}, {75, 50, 50}}
{{33, 11, 22}, {54, 18, 36}, {75, 25, 50}}
{{33, 18, 25}, {33, 18, 25}, {66, 36, 50}}
{{33, 54, 30}, {11, 18, 10}, {55, 90, 50}}
{{33, 27, 30}, {22, 18, 20}, {55, 45, 50}}
{{33, 18, 30}, {33, 18, 30}, {55, 30, 50}}
{{33, 33, 33}, {18, 18, 18}, {50, 50, 50}}
{{33, 18, 50}, {33, 18, 50}, {33, 18, 50}}
{{33, 33, 55}, {18, 18, 30}, {30, 30, 50}}
{{33, 22, 55}, {27, 18, 45}, {30, 20, 50}}
{{33, 11, 55}, {54, 18, 90}, {30, 10, 50}}
{{33, 33, 66}, {18, 18, 36}, {25, 25, 50}}
{{33, 54, 75}, {11, 18, 25}, {22, 36, 50}}
{{33, 27, 75}, {22, 18, 50}, {22, 18, 50}}
{{33, 18, 75}, {33, 18, 75}, {22, 12, 50}}
{{34, 34, 20}, {17, 17, 10}, {85, 85, 50}}
{{34, 17, 25}, {34, 17, 25}, {68, 34, 50}}
{{34, 34, 34}, {17, 17, 17}, {50, 50, 50}}
{{34, 17, 34}, {34, 17, 34}, {50, 25, 50}}
{{34, 34, 50}, {17, 17, 25}, {34, 34, 50}}
{{34, 17, 50}, {34, 17, 50}, {34, 17, 50}}
{{34, 34, 68}, {17, 17, 34}, {25, 25, 50}}
{{34, 17, 85}, {34, 17, 85}, {20, 10, 50}}
{{35, 40, 25}, {14, 16, 10}, {70, 80, 50}}
{{35, 20, 25}, {28, 16, 20}, {70, 40, 50}}
{{35, 16, 25}, {35, 16, 25}, {70, 32, 50}}
{{35, 10, 25}, {56, 16, 40}, {70, 20, 50}}
{{35, 56, 35}, {10, 16, 10}, {50, 80, 50}}
{{35, 35, 35}, {16, 16, 16}, {50, 50, 50}}
{{35, 28, 35}, {20, 16, 20}, {50, 40, 50}}
{{35, 14, 35}, {40, 16, 40}, {50, 20, 50}}
{{35, 40, 50}, {14, 16, 20}, {35, 40, 50}}
{{35, 20, 50}, {28, 16, 40}, {35, 20, 50}}
{{35, 16, 50}, {35, 16, 50}, {35, 16, 50}}
{{35, 10, 50}, {56, 16, 80}, {35, 10, 50}}
{{35, 56, 70}, {10, 16, 20}, {25, 40, 50}}
{{35, 35, 70}, {16, 16, 32}, {25, 25, 50}}
{{35, 28, 70}, {20, 16, 40}, {25, 20, 50}}
{{35, 14, 70}, {40, 16, 80}, {25, 10, 50}}
{{36, 30, 20}, {18, 15, 10}, {90, 75, 50}}
{{36, 20, 20}, {27, 15, 15}, {90, 50, 50}}
{{36, 12, 20}, {45, 15, 25}, {90, 30, 50}}
{{36, 10, 20}, {54, 15, 30}, {90, 25, 50}}
{{36, 36, 24}, {15, 15, 10}, {75, 75, 50}}
{{36, 12, 24}, {45, 15, 30}, {75, 25, 50}}
{{36, 15, 25}, {36, 15, 25}, {72, 30, 50}}
{{36, 45, 30}, {12, 15, 10}, {60, 75, 50}}
{{36, 30, 30}, {18, 15, 15}, {60, 50, 50}}
{{36, 18, 30}, {30, 15, 25}, {60, 30, 50}}
{{36, 15, 30}, {36, 15, 30}, {60, 25, 50}}
{{36, 54, 36}, {10, 15, 10}, {50, 75, 50}}
{{36, 36, 36}, {15, 15, 15}, {50, 50, 50}}
{{36, 18, 36}, {30, 15, 30}, {50, 25, 50}}
{{36, 20, 40}, {27, 15, 30}, {45, 25, 50}}
{{36, 12, 40}, {45, 15, 50}, {45, 15, 50}}
{{36, 45, 45}, {12, 15, 15}, {40, 50, 50}}
{{36, 27, 45}, {20, 15, 25}, {40, 30, 50}}
{{36, 30, 50}, {18, 15, 25}, {36, 30, 50}}
{{36, 15, 50}, {36, 15, 50}, {36, 15, 50}}
{{36, 10, 50}, {54, 15, 75}, {36, 10, 50}}
{{36, 36, 60}, {15, 15, 25}, {30, 30, 50}}
{{36, 30, 60}, {18, 15, 30}, {30, 25, 50}}
{{36, 18, 60}, {30, 15, 50}, {30, 15, 50}}
{{36, 12, 60}, {45, 15, 75}, {30, 10, 50}}
{{36, 36, 72}, {15, 15, 30}, {25, 25, 50}}
{{36, 45, 75}, {12, 15, 25}, {24, 30, 50}}
{{36, 15, 75}, {36, 15, 75}, {24, 10, 50}}
{{36, 54, 90}, {10, 15, 25}, {20, 30, 50}}
{{36, 45, 90}, {12, 15, 30}, {20, 25, 50}}
{{36, 27, 90}, {20, 15, 50}, {20, 15, 50}}
{{36, 18, 90}, {30, 15, 75}, {20, 10, 50}}
{{37, 14, 25}, {37, 14, 25}, {74, 28, 50}}
{{37, 37, 37}, {14, 14, 14}, {50, 50, 50}}
{{37, 14, 50}, {37, 14, 50}, {37, 14, 50}}
{{37, 37, 74}, {14, 14, 28}, {25, 25, 50}}
{{38, 26, 20}, {19, 13, 10}, {95, 65, 50}}
{{38, 13, 25}, {38, 13, 25}, {76, 26, 50}}
{{38, 38, 38}, {13, 13, 13}, {50, 50, 50}}
{{38, 19, 38}, {26, 13, 26}, {50, 25, 50}}
{{38, 26, 50}, {19, 13, 25}, {38, 26, 50}}
{{38, 13, 50}, {38, 13, 50}, {38, 13, 50}}
{{38, 38, 76}, {13, 13, 26}, {25, 25, 50}}
{{38, 19, 95}, {26, 13, 65}, {20, 10, 50}}
{{39, 12, 25}, {39, 12, 25}, {78, 24, 50}}
{{39, 26, 26}, {18, 12, 12}, {75, 50, 50}}
{{39, 13, 26}, {36, 12, 24}, {75, 25, 50}}
{{39, 36, 30}, {13, 12, 10}, {65, 60, 50}}
{{39, 18, 30}, {26, 12, 20}, {65, 30, 50}}
{{39, 12, 30}, {39, 12, 30}, {65, 20, 50}}
{{39, 39, 39}, {12, 12, 12}, {50, 50, 50}}
{{39, 12, 50}, {39, 12, 50}, {39, 12, 50}}
{{39, 39, 65}, {12, 12, 20}, {30, 30, 50}}
{{39, 26, 65}, {18, 12, 30}, {30, 20, 50}}
{{39, 13, 65}, {36, 12, 60}, {30, 10, 50}}
{{39, 36, 75}, {13, 12, 25}, {26, 24, 50}}
{{39, 18, 75}, {26, 12, 50}, {26, 12, 50}}
{{39, 39, 78}, {12, 12, 24}, {25, 25, 50}}
{{40, 11, 25}, {40, 11, 25}, {80, 22, 50}}
{{40, 44, 40}, {10, 11, 10}, {50, 55, 50}}
{{40, 40, 40}, {11, 11, 11}, {50, 50, 50}}
{{40, 20, 40}, {22, 11, 22}, {50, 25, 50}}
{{40, 22, 50}, {20, 11, 25}, {40, 22, 50}}
{{40, 11, 50}, {40, 11, 50}, {40, 11, 50}}
{{40, 10, 50}, {44, 11, 55}, {40, 10, 50}}
{{40, 40, 80}, {11, 11, 22}, {25, 25, 50}}
{{41, 10, 25}, {41, 10, 25}, {82, 20, 50}}
{{41, 41, 41}, {10, 10, 10}, {50, 50, 50}}
{{41, 10, 50}, {41, 10, 50}, {41, 10, 50}}
{{41, 41, 82}, {10, 10, 20}, {25, 25, 50}}
{{10, 20, 10}, {21, 42, 21}, {49, 98, 49}}
{{10, 10, 10}, {42, 42, 42}, {49, 49, 49}}
{{10, 28, 14}, {15, 42, 21}, {35, 98, 49}}
{{10, 14, 14}, {30, 42, 42}, {35, 49, 49}}
{{10, 12, 14}, {35, 42, 49}, {35, 42, 49}}
{{10, 35, 35}, {12, 42, 42}, {14, 49, 49}}
{{10, 30, 35}, {14, 42, 49}, {14, 42, 49}}
{{10, 15, 35}, {28, 42, 98}, {14, 21, 49}}
{{10, 42, 49}, {10, 42, 49}, {10, 42, 49}}
{{10, 21, 49}, {20, 42, 98}, {10, 21, 49}}
{{11, 11, 11}, {41, 41, 41}, {49, 49, 49}}
{{11, 41, 49}, {11, 41, 49}, {11, 41, 49}}
{{12, 24, 12}, {20, 40, 20}, {49, 98, 49}}
{{12, 12, 12}, {40, 40, 40}, {49, 49, 49}}
{{12, 20, 14}, {24, 40, 28}, {42, 70, 49}}
{{12, 16, 14}, {30, 40, 35}, {42, 56, 49}}
{{12, 10, 14}, {48, 40, 56}, {42, 35, 49}}
{{12, 30, 21}, {16, 40, 28}, {28, 70, 49}}
{{12, 24, 21}, {20, 40, 35}, {28, 56, 49}}
{{12, 15, 21}, {32, 40, 56}, {28, 35, 49}}
{{12, 12, 21}, {40, 40, 70}, {28, 28, 49}}
{{12, 40, 28}, {12, 40, 28}, {21, 70, 49}}
{{12, 32, 28}, {15, 40, 35}, {21, 56, 49}}
{{12, 20, 28}, {24, 40, 56}, {21, 35, 49}}
{{12, 16, 28}, {30, 40, 70}, {21, 28, 49}}
{{12, 48, 42}, {10, 40, 35}, {14, 56, 49}}
{{12, 30, 42}, {16, 40, 56}, {14, 35, 49}}
{{12, 24, 42}, {20, 40, 70}, {14, 28, 49}}
{{12, 40, 49}, {12, 40, 49}, {12, 40, 49}}
{{12, 20, 49}, {24, 40, 98}, {12, 20, 49}}
{{13, 13, 13}, {39, 39, 39}, {49, 49, 49}}
{{13, 39, 49}, {13, 39, 49}, {13, 39, 49}}
{{14, 28, 14}, {19, 38, 19}, {49, 98, 49}}
{{14, 14, 14}, {38, 38, 38}, {49, 49, 49}}
{{14, 38, 49}, {14, 38, 49}, {14, 38, 49}}
{{14, 19, 49}, {28, 38, 98}, {14, 19, 49}}
{{15, 15, 15}, {37, 37, 37}, {49, 49, 49}}
{{15, 37, 49}, {15, 37, 49}, {15, 37, 49}}
{{16, 24, 14}, {24, 36, 21}, {56, 84, 49}}
{{16, 18, 14}, {32, 36, 28}, {56, 63, 49}}
{{16, 12, 14}, {48, 36, 42}, {56, 42, 49}}
{{16, 32, 16}, {18, 36, 18}, {49, 98, 49}}
{{16, 16, 16}, {36, 36, 36}, {49, 49, 49}}
{{16, 48, 28}, {12, 36, 21}, {28, 84, 49}}
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