Halmazok -
megoldások
A 2.1., pozitív egész számos feladat
megoldása
100 ilyen részhalmaz
van:
{1, 2, 3, 6}
{1, 2, 3, 12}
{1, 2, 4, 7}
{1, 2, 5, 8}
{1, 2, 5, 12}
{1, 2, 6, 9}
{1, 2, 7, 10}
{1, 2, 8, 11}
{1, 2, 9, 12}
{1, 3, 4, 8}
{1, 3, 5, 6}
{1, 3, 6, 8}
{1, 3, 6, 10}
{1, 3, 7, 10}
{1, 3, 8, 12}
{1, 4, 5, 10}
{1, 4, 6, 11}
{1, 4, 7, 9}
{1, 4, 7, 12}
{1, 4, 9, 10}
{1, 5, 6, 8}
{1, 5, 6, 12}
{1, 5, 9, 10}
{1, 5, 9, 12}
{1, 6, 8, 9}
{1, 6, 9, 11}
{1, 7, 8, 12}
{1, 7, 10, 12}
{1, 8, 11, 12}
{1, 9, 11, 12}
{2, 3, 4, 9}
{2, 3, 5, 10}
{2, 3, 6, 7}
{2, 3, 6, 11}
{2, 3, 7, 9}
{2, 3, 7, 12}
{2, 3, 8, 11}
{2, 4, 5, 9}
{2, 4, 5, 11}
{2, 4, 6, 12}
{2, 4, 9, 12}
{2, 5, 6, 7}
{2, 5, 8, 9}
{2, 5, 8, 10}
{2, 5, 11, 12}
{2, 6, 9, 10}
{2, 6, 10, 12}
{2, 7, 8, 11}
{2, 7, 9, 10}
{2, 8, 10, 12}
{2, 8, 11, 12}
{3, 4, 5, 6}
{3, 4, 5, 8}
{3, 4, 5, 12}
{3, 4, 6, 11}
{3, 4, 7, 10}
{3, 4, 8, 9}
{3, 4, 9, 11}
{3, 5, 6, 7}
{3, 5, 7, 10}
{3, 5, 9, 10}
{3, 5, 10, 12}
{3, 6, 7, 8}
{3, 6, 7, 12}
{3, 6, 10, 11}
{3, 7, 8, 9}
{3, 7, 8, 10}
{3, 7, 11, 12}
{3, 8, 9, 10}
{3, 8, 9, 12}
{3, 9, 10, 11}
{3, 10, 11, 12}
{4, 5, 6, 9}
{4, 5, 6, 10}
{4, 5, 7, 12}
{4, 5, 9, 12}
{4, 6, 7, 11}
{4, 6, 8, 9}
{4, 6, 10, 12}
{4, 6, 11, 12}
{4, 7, 8, 9}
{4, 7, 9, 10}
{4, 8, 9, 11}
{4, 9, 11, 12}
{5, 6, 7, 9}
{5, 6, 7, 10}
{5, 6, 7, 12}
{5, 6, 8, 11}
{5, 6, 9, 10}
{5, 7, 8, 12}
{5, 7, 11, 12}
{5, 8, 9, 11}
{5, 9, 10, 12}
{6, 7, 9, 11}
{6, 7, 10, 12}
{6, 7, 11, 12}
{6, 8, 10, 12}
{6, 9, 10, 11}
{7, 8, 9, 12}
{7, 10, 11, 12}
A 2.2., háromszögszámos feladat megoldása
56 ilyen részhalmaz
van:
{1, 3, 6, 10}
{1, 3, 10, 21}
{1, 3, 10, 28}
{1, 6, 21, 28}
{1, 6, 45, 78}
{1, 10, 21, 28}
{1, 10, 28, 45}
{1, 10, 28, 66}
{1, 10, 55, 66}
{1, 15, 28, 36}
{1, 15, 28, 66}
{1, 15, 36, 78}
{1, 21, 28, 55}
{1, 28, 36, 55}
{1, 28, 45, 66}
{3, 6, 15, 21}
{3, 6, 15, 36}
{3, 6, 15, 66}
{3, 6, 21, 78}
{3, 6, 36, 45}
{3, 10, 15, 28}
{3, 10, 21, 36}
{3, 15, 21, 66}
{3, 15, 21, 78}
{3, 15, 36, 66}
{3, 15, 66, 78}
{3, 21, 36, 45}
{3, 21, 36, 66}
{3, 21, 45, 66}
{3, 28, 36, 45}
{3, 36, 45, 78}
{6, 10, 28, 36}
{6, 10, 28, 66}
{6, 10, 36, 78}
{6, 15, 21, 28}
{6, 15, 21, 66}
{6, 15, 36, 78}
{6, 15, 45, 66}
{6, 15, 66, 78}
{6, 21, 28, 55}
{6, 21, 36, 45}
{6, 45, 66, 78}
{10, 15, 45, 55}
{10, 28, 36, 66}
{10, 28, 66, 78}
{15, 21, 66, 78}
{15, 28, 45, 66}
{15, 36, 45, 66}
{15, 36, 66, 78}
{21, 28, 36, 55}
{21, 28, 55, 78}
{21, 36, 45, 66}
{21, 36, 45, 78}
{21, 45, 66, 78}
{21, 55, 66, 78}
{28, 36, 66, 78}
A 2.3., tetraéderszámos feladat megoldása
37 ilyen részhalmaz
van:
{1, 4, 10, 35}
{1, 4, 35, 120}
{1, 20, 35, 56}
{1, 20, 35, 84}
{1, 20, 84, 120}
{1, 20, 165, 364}
{1, 35, 84, 120}
{1, 35, 120, 364}
{1, 120, 165, 286}
{1, 120, 165, 364}
{4, 10, 20, 286}
{4, 10, 220, 286}
{4, 20, 56, 120}
{4, 56, 120, 220}
{4, 84, 220, 364}
{10, 20, 84, 286}
{10, 35, 84, 165}
{10, 35, 120, 165}
{10, 35, 120, 220}
{10, 56, 84, 165}
{10, 56, 220, 286}
{10, 56, 220, 364}
{10, 84, 220, 286}
{10, 120, 286, 364}
{10, 165, 286, 364}
{10, 220, 286, 364}
{20, 35, 165, 220}
{20, 56, 84, 120}
{20, 56, 120, 364}
{20, 84, 120, 364}
{35, 84, 120, 286}
{35, 84, 165, 220}
{35, 165, 220, 364}
{56, 84, 120, 220}
{56, 84, 120, 286}
{56, 84, 120, 364}
{56, 84, 165, 220}
A 2.4., négyzetszámos feladat megoldása
19 ilyen részhalmaz
van:
{1, 4, 9, 49}
{1, 16, 49, 81}
{1, 16, 64, 81}
{1, 25, 49, 100}
{1, 49, 100, 144}
{4, 9, 36, 49}
{4, 9, 49, 64}
{4, 9, 64, 121}
{4, 25, 100, 121}
{4, 36, 81, 121}
{9, 16, 25, 100}
{9, 25, 49, 64}
{16, 25, 36, 49}
{16, 25, 36, 121}
{25, 36, 49, 100}
{25, 36, 49, 121}
{25, 36, 64, 100}
{25, 64, 81, 100}
{49, 64, 81, 100}