X ,Y and Z are three friends and they decided to go out for picnic. Each of them rides bicycle and wears a hat. Each one wear a hat of the other friend and ride the bicycle of another friend. X is wearing Z's hat. Find who is riding X's bicycle?
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Examine the cases,
ATQ,
X ---> hat of Z
Therefore,
Y ---> hat of X [ he cannot wear his own hat and Z's hat is with X]
---> cycle of Z [hat and cycle cannot be of the same friend and he cannot ride his own cycle]
Therefore,
Z ---> hat of Y [it is the only hat left]
---> cycle of X [ only cycle left]
Now it is clear that X's cycle is with Z.