Ponder This Challenge - August 2000 - Six Card Cribbage

Ponder This Challenge:

Here are some cribbage puzzles proposed by Denis Borris. (Thanks, Denis!) For the rules of cribbage you can visit the site
http://www.cs.montana.edu/~paxton/cribbage.html
Caveat: although these rules refer to a 61-point game, here we are playing a 121-point game.

Puzzle 1:
Did you know it is possible for you to win 121 to 8 after 2 rounds only?
(That is, the cards are dealt twice, in a two-handed game. The opponents cooperate to make this happen; optimal play is not assumed.)

Puzzle 2:
During the first pegging round of a four-handed game (two against two), the score reaches 43-0.

Puzzle 3:
(A two-handed game):
The game starts and Jack wins first deal.
The first pegging round just ended; John pegged ZERO points.
But Jack (as usual!) pegged the MAXIMUM possible points.
What 4 cards did Jack have, and what 4 cards did John have?
Hint: Jack did not have a 5.

Puzzle 4:
6card Crib
New cribbage game:
-each player gets 6 cards
-that's it: no discards or deck cutting
-no change in the pegging and point counting
OK; first deal: your opponent plays first;
this first deal ends with you getting the maximum
points possible while your opponent gets ZERO points;
includes the pegging points and the hand points.
What are your 6 cards?

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solution

• Click here to view the solution

  WINNING 121 TO 8 AFTER ONLY 2 ROUNDS
  Did you know it is possible for you to win 121 to 8 after 2 rounds only?
  You win the cut and deal first.
  Notes: Jd and 5d = jack and 5 of diamonds (suits don't matter after). Bracketed numbers like (3) is the order cards played during pegging.

  	YOU			HIM/HER
  		POINTS			POINTS
  CRIB:	5 5 5 Jd	21
  			NIB: 5d
  HAND:	4 4 4 6	29		4 9 10 K	4
  	(2) 6	2		(1) 9
  	(4) 4	2		(3) 4
  	(5) 4	6		GO
  	(6) 4	14		(7) 10
  				(8) K	1
  ROUND#1:		74			5
  CRIB:				4 4 7 7	TOO LATE!
  			NIB: 4
  HAND:	5 5 5 6	23		4 5 Q K	TOO LATE!
  	(1) 6			(2) 4
  	(3) 5	5		(4) 5	2
  	(5) 5	6		GO
  	(6) 5	13		(7) Q
  				(8) K	1
  ROUND#2:		47			3
  TOTAL:		121			8

  ---

  43 TO 0 AFTER 1ST PEGGING ROUND
  Playing 2 against 2, and during the 1st pegging round of a deal...a team can get 43 points and the opponents ZERO.
  PARTNERS : A-C & B-D
  B plays first:

  	A 1 1 2 2
  D 2 10 K Q		B 9 10 J K
  	C 1 1 2 9

  Player		Card	OnTable	Points	Cumulative
  B		9	9	0	0
  C		9	18	2	2
  D		2	20	0	2
  A		2	22	2	4
  B	GO
  C		2	24	6	10
  D	GO
  A		2	26	12	22
  B	GO
  C		1	27	0	22
  D	GO
  A		1	28	2	24
  B	GO
  C		1	29	6	30
  D	GO
  A		1	30	13	43

  ...THE OPPONENTS QUIT!!

  ---

  15 two, 15 four, and the rest don't score
  Well, well: cribbage again.
  The game starts and Jack wins first deal.
  The first pegging round just ended; John pegged ZERO points.
  But Jack (as usual!) pegged the MAXIMUM possible points.
  What 4 cards did Jack have, and what 4 cards did John have?
  Hint: Jack did not have a 5.

  (n) represents the order in which the cards were played):

  hands:	1 3 5 7		2 3 4 6
  	JOHN		JACK	ON TABLE	POINTS	TOTAL POINTS	EXPLANATION
  	(1) 3		(2) 3	6	2	2	pair
  	(3) 5		(4) 4	15	5	7	run(3-5),15
  	(5) 1		(6) 2	18	5	12	run(1-5)
  	(7) 7		(8) 6	31	9	21	run(1-7),31

  ---

  6card Crib
  New cribbage game:

  • each player gets 6 cards
    • that's it: no discards or deck cutting

      • no change in the pegging and point counting
        OK; first deal: your opponent plays first; this first deal ends with you getting the maximum points possible while your opponent gets ZERO points; includes the pegging points and the hand points.
        What are your 6 cards?
        Enter in ascending order: 1-2-3-4-5-6
        (Jacks Queens Kings = 10)

        Brackets ( ) indicate total on table, [ ] indicate pegging points.

        	OPPONENT				ME
        Cards (order pegged)	9 4 3 10 7 K				6 4 5 5 6 4
        1st pegging round	9	(9)			6	(15)	[2]
        	4	(19)			4	(23)	[2]
        	3	(26)			5	(31)	[5]
        2nd pegging round	10	(10)			5	(15)	[2]
        	7	(22)			6	(28)	[4]
        3rd pegging round	K	(10)			4	(14)	[1]
        Pegging points:			0				16
        Hand points - 8 15's:							16
        - 8 runs:							24
        - 3 pairs:							6
        TOTAL POINTS			0				62

        Note: could be played slightly different, and opponent could have a different card or two, but YOU need 445566 !!

  ---

  If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solvers

• Dave Biggar (8.21.2000 @ 9:03 AM EDT)