A very special island is inhabited only by knights and liars. Knights always tell the truth, and liars always lie.
Nine inhabitants of the island: Mel, Bart, Sue, Betty, Rex, Zeke, Sally, Zoey and Homer are busy at a conversation. A visitor from a neighboring island stops by and asks each of the nine inhabitants their respective identities. They say:
- Mel: "Only a liar would say that Sally is a liar."
- Bart: "Rex is a liar."
- Sue: "Mel and Homer are liars."
- Betty: "I know that I am a knight and Sally is a liar."
- Rex : "Betty and I are both knights."
- Zeke: "At least one of the following is true: that Sally is a knight or that Sue is a knight."
- Sally:"It's false that Betty is a liar."
- Zoey: "It's not the case that Sue is a liar."
- Homer: "Betty is a liar or Zeke is a liar."
Determine the type of each of the inhabitants from the abovementioned statements.
Bart and Homer are the only knights; the rest are liars.
FOR k1 = 0 TO 1
FOR k2 = 0 TO 1
FOR k3 = 0 TO 1
FOR k4 = 0 TO 1
FOR k5 = 0 TO 1
FOR k6 = 0 TO 1
FOR k7 = 0 TO 1
FOR k8 = 0 TO 1
FOR k9 = 0 TO 1
IF k1 = k7 THEN
IF k2 = 1 - k5 THEN
IF k3 = ABS(k1 = 0 AND k9 = 0) THEN
IF k4 = 0 OR k7 = 0 THEN
IF k5 = 0 OR k4 = 1 THEN
IF k6 = ABS(k7 = 1 OR k3 = 1) THEN
IF k7 = k4 THEN
IF k8 = k3 THEN
IF k9 = ABS(k4 = 0 OR k6 = 0) THEN
PRINT k1; k2; k3; k4; k5; k6; k7; k8; k9
lists the types in order of appearance, with 0=liar and 1=knight:
0 1 0 0 0 0 0 0 1
Posted by Charlie
on 2010-02-06 14:09:13