perplexus.info :: Liars and Knights : Knave Contest

Knave Contest (Posted on 2008-04-03)

Alex, Bert, Carl, Dave, Eddy, Fred, Gary, and Hank have just finished a single elimination contest. They are all knaves, meaning each one alternates between making true and false statements. Each person makes two statements about the contest as follows:

Alex:
1: I played against Carl in the first round.
2: I lost in round 2.

Bert:
1: I played against Dave in the first round.
2: I won the contest.

Carl:
1: I played against Eddy in the first round.
2: I lost in round 1.

Dave:
1: I played against Gary in the first round.
2: I lost in round 2.

Eddy:
1: I played against Fred in the first round.
2: I lost in round 2.

Fred:
1: I played against Hank in the first round.
2: I won the contest.

Gary:
1: I played against Bert in the first round.
2: I lost in round 1.

Hank:
1: I played against Alex in the first round.
2: I lost in round 2.

The contest was setup in a way so that the only way Carl and Dave would play against each other was if they were the final two contestants.

Determine the pairs of players for all seven games in the contest with the given statements.

 Round 1 | Round 2 | Round 3 | Winner

_________
         |_________
_________|         |
                   |_________
_________          |         |
         |_________|         |
_________|                   |
                             |_________
_________                    |
         |_________          |
_________|         |         |
                   |_________|
_________          |
         |_________|
_________|

See The Solution Submitted by Brian Smith

Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Sol

| Comment 7 of 8 |

<TABLE style="WIDTH: 244pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=325 border=0 x:str> <COLGROUP> <COL style="WIDTH: 194pt; mso-width-source: userset; mso-width-alt: 9435" width=258> <COL style="WIDTH: 50pt; mso-width-source: userset; mso-width-alt: 2450" width=67> <TBODY> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 194pt; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" width=258 height=18>Alex:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 50pt; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=67></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1: I played against Carl in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18>2: I lost in round 2.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18>Bert:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18>1: I played against Dave in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18>2: I won the contest.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18>Carl:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18>1: I played against Eddy in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2: I lost in round 1.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 13.5pt" height=18> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" height=18></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>Dave:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1: I played against Gary in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2: I lost in round 2.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>Eddy:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1: I played against Fred in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2: I lost in round 2.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>Fred:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1: I played against Hank in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2: I won the contest.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>Gary:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1: I played against Bert in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2: I lost in round 1.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>Hank:</TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1: I played against Alex in the first round.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">f</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl65 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>2: I lost in round 2.</TD> <TD class=xl67 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent">t</TD></TR> <TR style="HEIGHT: 12.75pt" height=17> <TD class=xl66 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17></TD> <TD class=xl68 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent"></TD></TR></TBODY></TABLE>

Posted by Andre on 2010-05-24 18:53:32

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