All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
A Strange Game of Poker (Posted on 2009-08-11) Difficulty: 3 of 5
You start with a standard deck of cards. Each card is assigned a numeric value from 1 to 52 as follows:

A through K of Clubs = 1 through 13
A through K of Diamonds = 14 through 26
A through K of Spades = 27 through 39
A through K of Hearts = 40 through 52

Each player draws two cards and calculates the cube of the sum of the values of the two cards. Each player then selects five or less non-zero digits from their answer to form their Poker hand. Hands are evaluated solely on the digits, 1 is low and 9 is high, and there are no suits involved. For example: One player draws the 4 of Clubs (4) and the 6 of Diamonds (19); 4 + 19 = 23, 23^3 = 12167, the player has a pair of 1's. A second player draws the Ace of Dimaonds (14) and the Ace of Clubs (1); 14 + 1 = 15, 15^3 = 3375 and she wins the hand with a pair of 3's.

Given these rules, what is the best possible Poker hand a player can have and how many possible combinations of cards will yield that hand?

See The Solution Submitted by Sing4TheDay    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution agrees | Comment 2 of 3 |

The version of the program below seeks full houses, after previous versions unsuccessfully looked for 5 or 4 of a kind. The current version finds that a physical hand with a total of 92 will produce the cube 778688, and therefore a full house of 88877, the best that can be done.

The program also checks for 4-straights, having unsuccessfully looked for regular straights of 5 cards, just to check that its straight finding mechanism is working properly.

CLS
FOR s = 3 TO 103
   t = s * s * s
   h$ = LTRIM$(STR$(t))
   DO
     ix = INSTR(h$, "0")
     IF ix = 0 THEN EXIT DO
     h$ = LEFT$(h$, ix - 1) + MID$(h$, ix + 1)
   LOOP
   'look for full house
   FOR d = 1 TO 9
    dig$ = MID$("198765432", d, 1)
    ct = 0
    psn = 0
    DO
      ix = INSTR(psn + 1, h$, dig$)
      IF ix THEN ct = ct + 1:  ELSE EXIT DO
      psn = ix
    LOOP
    IF ct >= 3 THEN
     pdig$ = dig$
     FOR d2 = 1 TO 9
      dig$ = MID$("198765432", d2, 1)
      IF dig$ <> pdig$ THEN
        ct = 0
        psn = 0
        DO
          ix = INSTR(psn + 1, h$, dig$)
          IF ix THEN ct = ct + 1:  ELSE EXIT DO
          psn = ix
        LOOP
        IF ct >= 2 THEN
          PRINT s, t, h$
        END IF
      END IF
     NEXT
    END IF
   NEXT

    'just for curiosity, check for straights (4-straights to be exact)
    h2$ = h$
    DO
     ix = INSTR(h2$, "1")
     IF ix = 0 THEN EXIT DO
     h2$ = LEFT$(h2$, ix - 1) + "A" + MID$(h2$, ix + 1)
    LOOP
    IF LEN(h$) >= 4 THEN
      DO
       done = 1
       FOR i = 1 TO LEN(h2$) - 1
        IF MID$(h2$, i, 1) > MID$(h2$, i + 1, 1) THEN
          hold$ = MID$(h2$, i, 1)
          MID$(h2$, i, 1) = MID$(h2$, i + 1, 1)
          MID$(h2$, i + 1, 1) = hold$
          done = 0
        END IF
       NEXT
      LOOP UNTIL done
      ct = 1
      FOR i = 2 TO LEN(h2$)
       a = VAL(MID$(h2$, i - 1, 1)): b = VAL(MID$(h2$, i, 1))
       SELECT CASE b - a
        CASE 0
        CASE 1
         ct = ct + 1
        CASE ELSE
         ct = 1
       END SELECT
       IF ct = 4 THEN EXIT FOR
      NEXT
      IF ct >= 4 THEN
         PRINT s, t, h$, "S"
      END IF
    END IF
NEXT

The results:

54            157464       157464        S
65            274625       274625        S
66            287496       287496        S
76            438976       438976        S
77            456533       456533        S
92            778688       778688

Those marked with S are just the 4-straights, and don't count. The answer is the last line, the full house 88877.


  Posted by Charlie on 2009-08-11 17:54:45
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information