# logic word puzzle

• Oct 20th 2008, 02:01 PM
boomshine57th
logic word puzzle
hey guys. who is interested in a logic puzzle? i still cant work it out :( help me please

four suspects W,X,Y and Z were rounded up for questioning conserning a break in. it was known that at least one was guilty, and that no on outside the 4 was involved. the following facts were established:

a) W is definatelly innocent
b)if X was guilty, then he had exactly one accomplice
c) if Y was guilty, then he had exactly two accomplice

is Z guilty or not?
• Oct 20th 2008, 02:37 PM
ticbol
Quote:

Originally Posted by boomshine57th
hey guys. who is interested in a logic puzzle? i still cant work it out :( help me please

four suspects W,X,Y and Z were rounded up for questioning conserning a break in. it was known that at least one was guilty, and that no on outside the 4 was involved. the following facts were established:

a) W is definatelly innocent
b)if X was guilty, then he had exactly one accomplice
c) if Y was guilty, then he had exactly two accomplice

is Z guilty or not?

If X is guilty, then his accomplice could be Y or Z
If Y is guilty, then his accomplices can only be X and Z

Is Z guilty?

Not sure. Because X could be the guilty person and Y is his accomplice.
• Oct 20th 2008, 02:40 PM
jaydee323
z is guilty

if y is guilty then so are x and z

if x is guilty then so is z ( because if y was guilty al three would be guilty)
• Oct 20th 2008, 02:57 PM
Soroban
Hello, boomshine57th!

Quote:

Four suspects $\displaystyle W,X,Y\text{ and }Z$ were rounded up for questioning concerning a break-in.
It was known that at least one was guilty, and that no one outside the 4 was involved.
The following facts were established:

(a) $\displaystyle W$ is definitely innocent
(b) if $\displaystyle X$ was guilty, then he had exactly one accomplice
(c) if $\displaystyle Y$ was guilty, then he had exactly two accomplices

Is $\displaystyle Z$ guilty or not?

From (a), the only suspects are: .$\displaystyle X,Y,Z$

If (c) is true, then $\displaystyle Y$ is guilty, and $\displaystyle X$ and $\displaystyle Y$ were accomplices.
. . Then all three are guilty. ($\displaystyle X$ had two accomplices; $\displaystyle Z$ had two accomplices.)
Hence, (b) is not true.

Therefore, (c) is not true: $\displaystyle Y$ is innocent.
. . The only suspects are: .$\displaystyle X\text{ and }Z$

$\displaystyle X$ is either (1) guilty or (2) innocent.

(1) If $\displaystyle X$ is guilty, then (b) says he had one accomplice; it must be $\displaystyle Z$.
. . Hence, $\displaystyle Z$ is guilty.

(2) If $\displaystyle X$ is innocent, then $\displaystyle Z$ is the only remaining suspect.
. . Hence, $\displaystyle Z$ is guilty.

Therefore, $\displaystyle Z$ is guilty.

• Oct 20th 2008, 03:01 PM
boomshine57th
i love your logic! thats really good! thank you ever so much! (star)