# Xeno, Yves, and Zahara are best friends celebrating one of their own birthdays. They make the following statements...

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Xeno, Yves, and Zahara are best friends celebrating one of their own birthdays. They make the following statements:

Xeno says, "It's Yves' birthday!"
Yves says, "It's not Xeno's birthday!"
Zahara whispers, "It's __'s birthday", but so quietly that you can't make out which of the three names she said.

If I told you how many true statements were made, then you still wouldn't know whose birthday it is. Now that you know that, if I told you what Zahara said then you'd know whose birthday it is.

Whose birthday is it?

posted Feb 4, 2019

Yves'

Lets analyse possible outcomes.
See picture below first:

Here is the all possible statements and outcomes for each possible number of True or False number of statements.- T0 meaning no true, F3 meaning 3 false statements etc.
As we see, regardless what Zahara says, there is single name as outcome if 0, 1 or 3 True statements made.
"If I told you how many true statements were made, then you still wouldn't know whose birthday it is"- it means the number of true statements is 2, otherwise we would know the name.
Now, if Zahara's statement was her own name it would not make sense as in this case 1. it would cause conflict of statements with 2 possible names, 2. Zahara would not say "It's Zahara's birthday". Zahara whispered Xeno's name which becomes false statement giving Yves name as outcome.

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