Pick-7 MM and EHB systems
pick-7, 32 numbers, seven 3 if 3 guarantee, 992
combinations (MM, EHB)
(the best known single 3 if 3 guarantee system is in 165
combinations)(7*165=1155)
(992 is the minimum number of combinations required for balance of
up to 3-wins)
pick-7, 32 numbers, thirty five 3 if 3 guarantee,
4960 combinations (MM, EHB)
(also four 4 if 4; the best known single 4 if 4 guarantee system
is in 1387 combinations)(4*1387=5548)
(also twenty 4 if 5; the best known single 4 if 5 guarantee system is in 538
combinations)(20*538=10760)
pick-7, 28 numbers, 5 if 5 guarantee, 4680
combinations (MM, EHB, MAC)
(also eight 4 if 4; the best known single 4
if 4 guarantee system is in 793 combinations)(8*793=6344)
(also six 5 if 6; the best known single 5 if 6 guarantee
system is in 2272 combinations)(6*2272=13632)
pick-7, 27 numbers, seven 4 if 4 guarantee, 3510
combinations (MM, EHB, MAC)
(the best known single 4 if 4 guarantee system is 635
combinations)(7*635=4445)
pick-7, 26 numbers, thirty five 3 if 3 guarantee,
2600 combinations (MM, EHB, MAC)
(the best known single 3 if 3 guarantee system is in 94
combinations)(35*94=3290)
(also six 4 if 4; the best known single 4 if 4 guarantee system is
in 551 combinations)(6*551=3306)
pick-7, 24 numbers, three 5 if 5 guarantee, 6072
combinations (MM, EHB)
(the best known single 5 if 5 guarantee system is 2576
combinations)(3*2576=7728)
(also MM with two 6 if 7
guarantee; the best known single 6 if 7 guarantee system
is 4829 combinations)(2*4829=9658)
pick-7, 23 numbers, 4 if 4 guarantee, 253
combinations (MM, EHB)
pick-7, 23 numbers, seventeen 4 if 4 guarantee, 4301
combinations (MM, EHB)
(also sixteen 5 if 6; the best known single 5 if 6 guarantee
system is 686 combinations)(16*686=10976)
pick-7, 23 numbers, three 5 if 5 guarantee, 4807
combinations (MM, EHB)
(the best known single 5 if 5 guarantee system is in 1948
combinations)(3*1948=5844)
(253 combinations are repeated three times each; still the best
and MM with the triple 5 if 5 guarantee)
(also two 6 if 7; the best single 6 if 7 guarantee system is in
3582 combinations)(2*3582=7164)
pick-7, 22 numbers, four 3 if 3 guarantee, 176
combinations (MM, EHB, MAC)
(the best known single 3 if 3 guarantee system is 59
combinations)(4*59=236)
pick-7, 22 numbers, 5 if 5 guarantee, 1584
combinations (MM, EHB up to 3-wins)
(also thirty six 3 if 3 - MM)
(also six 5 if 6; the best known single 5 if 6 guarantee system is
in 526 combinations)(6*526=3156)
(also six 4 if 4; the best known single 4 if 4 guarantee system is
in 580 combinations)(6*580=3480)
(also twenty one 5 if 7; the best known single 5 if 7 guarantee
system is in 246 combinations)(21*246=5166)
pick-7, 20 numbers, thirty five 3 if 3 guarantee,
1140 combinations (MM, EHB up to 3-wins)
(the best known single 3 if 3 guarantee system is in 45
combinations)(35*45=1575)
pick-7, 19 numbers, thirty five 3 if 3 guarantee,
969 combinations (MM, EHB up to 3-wins)
(the best known single 3 if 3 guarantee system is in 35
combinations)(35*35=1225)
pick-7, 18 numbers, six 5 if 5 guarantee, 2448
combinations (MM, EHB)
(the best known single 5 if 5 system is in 548
combinations)(6*548=3288)
(also six 6 if 7; the best single 6 if 7 guarantee system is in
654 combinations)(6*654=3924)
pick-7, 18 numbers, eighteen 5 if 5 guarantee,
7344 combinations (MM, EHB)
(also eighteen 6 if 7; the best single 6 if 7
guarantee system is in 654 combinations)(18*654=11772)
pick-7, 17 numbers, six 4 if 4 guarantee, 408
combinations (MM, EHB)
(the best known single 4 if 4 system is in 99
combinations)(6*99=594)
pick-7, 17 numbers, twenty two 4 if 4 guarantee, 1496
combinations (MM, EHB)
(the best known single 4 if 4 system is in 99
combinations)(22*99=2178)
(also four 5 if 5; the best single 5 if 5 guarantee system is in
398 combinations)(4*398=1592)
(also four 6 if 7; the best single 6 if 7 guarantee system is in
444 combinations)(4*444=1776)
pick-7, 17 numbers, forty six 4 if 4 guarantee, 3128
combinations (MM, EHB)
(the best known single 4 if 4 system is in 99
combinations)(46*99=4554)
(also twelve 6 if 7; the best single 6 if 7 guarantee system is in
444 combinations)(12*444=5328)
pick-7, 17 numbers, two 6 if 6 guarantee, 3536
combinations (MM, EHB up to 6-wins!)
(the best known single 6 if 6 guarantee system is in 2048
combinations)(2*2048=4096)
(also twelve 5 if 5; the best known single 5 if 5 guarantee system
is in 398 combinations)(12*398=4776)
(also fourteen 6 if 7; the best known single 6 if 7 guarantee
system is in 444 combinations)(14*444=6216)
The system would be MM in the entire range of guarantees
(including fourteen 6 if 7)!
It has 408 combinations repeated, yet it is the best possible
system with this guarantee.
A system without repeated combinations and the same guarantee is
unknown.
pick-7, 16 numbers, fifteen 5 if 5 guarantee, 3120
combinations (MM, EHB)
(the best known 5 if 5 single guarantee system is 283
combinations)(15*283=4245)
(also sixteen 6 if 7; the best known single 6 if 7 guarantee
system is 293 combinations)(16*293=4688)
pick-7, 16 numbers, ten 5 if 5 guarantee, 2080
combinations (MM, EHB)
(the best known single 5 if 5 guarantee system is in 283
combinations)(10*283=2830)
(also twelve 6 if 7 guarantee; the best single 6 if 7 guarantee
system is in 293 combinations)(12*293=3516)
It has 240 combinations repeated, still the best and MM with the
stated guarantee.
A system without repeated combinations and the same
main guarantee is also possible:
pick-7, 16 numbers, ten 5 if 5 guarantee, 2080
combinations (MM, EHB)
(the best known single 5 if 5 guarantee system is in 283
combinations)(10*283=2830)
(also ten 6 if 7; the best known single 6 if 7 guarantee system is
in 293 combinations)(10*293=2930)
(it could look slightly weaker than the one with repeated
combinations in terms of 6 if 7,
but in some cases it would give more 6 if 7; up to 15, while the
other one gives up to 14)
pick-7, 16 numbers, fifteen 3 if 3 guarantee, 240
combinations (MM, EHB, MAC)
(the best known single 3 if 3 guarantee system is in
24 combinations)(15*24=360)
pick-7, 16 numbers, four 4 if 4 guarantee, 240
combinations (MM, EHB up to 3-wins)
(the best known single guarantee 4 if 4 system is in 76
combinations)(4*76=304)
(also fifteen 3 if 3 - MM)
(also twenty 4 if 5; the best known single guarantee system is in
28 combinations)(20*28=560)
This system would be different than the one above it (better
4-wins guarantee, but not MAC).
pick-7, 16 numbers, ten 3 if 3 guarantee, 160
combinations (MM, EHB up to 3-wins)
(the best known single 3 if 3 guarantee system is in 24
combinations)(10*24=240)
pick-7, 15 numbers, fifteen 5 if 5 guarantee, 2145
combinations (MM, EHB)
(the best known single 5 if 5
guarantee system is in 189 combinations)(15*189=2835)
(also eighteen 6 if 7; the best known single 6 if 7 guarantee
system is in 180 combinations)(18*180=3240)
pick-7, 15 numbers, thirty 4 if 4 guarantee, 1170
combinations (MM, EHB)
(the best known single 4 if 4 system is in 57
combinations)(30*57=1710)
pick-7, 14 numbers, twelve 5 if 5 guarantee, 1144
combinations (MM, EHB)
(the best known 5 if 5 single guarantee system is in 138
combinations)(12*138=1656)
(also eighteen 6 if 7; the best known single 6 if 7 guarantee
system is in 100 combinations)(18*100=1800)
(also forty 4 if 4; the best known single 4 if 4 guarantee system
is in 44 combinations)(40*44=1760)
pick-7, 14 numbers, five 3 if 3 guarantee, 52
combinations (MM, EHB)
(also two 5 if 6; the
best known single 5 if 6 guarantee system is in 35
combinations)(2*35=70)
(also nine 5 if 7; the best known single 5 if 7 guarantee system
is in 14 combinations)(9*14=126)
(also eight 4 if 5; the best known single 4 if 5 guarantee system
is in 14 combinations)(8*14=112)
pick-7, 12 numbers, twenty eight 4 if 4 guarantee,
396 combinations (MM, EHB)
(the best known single 4 if 4 guarantee system is in
24 combinations)(28*24=672)
(also ten 5 if 5; the best known
single 5 if 5 guarantee system is in 59 combinations)(10*59=590)
(also twenty 6 if
7; the best known single 6 if 7
guarantee system is in 35 combinations)(20*35=700)
pick-7, 12 numbers, twenty one 3 if 3 guarantee, 132
combinations (MM, EHB)
(the best known (MM) single
3 if 3 guarantee system is in 11 combinations)(21*11=231)
(also three 5 if 5; the best known single
5 if 5 guarantee system is in 59 combinations)(3*59=177)
(also six 6 if 7;
the best known single 6 if 7 guarantee system is in 35
combinations)(6*35=210)
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