good chemistry is complicated,and a little bit messy -LW PerlMonks

### Re: Generating all 5-card hands

by 5mi11er (Deacon)
 on May 18, 2005 at 20:48 UTC ( #458435=note: print w/replies, xml ) Need Help??

in reply to Generating all 5-card hands

Forget brute force, using logic to try to create a hand that has no points:

• All 10, J, Q, K's are eliminated

• Because 6+9=15 and 7+8=15, we may only take one from each group above 5
ie. 6 & 8, 7 & 9 or 8 & 9. 6 & 7 gives a three card run.

• This means we MUST use at least 2 cards less than 5.

• A, 2, no 3, that would be a 3 card run, 4, 5
can't have a 6, 6+4=10, or 7, 7+2+A=10, or 8, or 9 for same reasons. Dead end.

• 2, 3, no 4, 5, 6 ok, no 8 allowed, nor 7. Dead end.

• A, 3, 5, 8, --> Dead end.

• A, 4, 5, 7, --> Dead end.

• 2, 4, 5, 7, no 9, 9+2+4=15. Dead end.

this elminates all possible hands.

-Scott

Update: L~R beat me to what this essentially boils down to up in this node posted just before I'd managed to finish mine.

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