William lives in a street with house-numbers 8 up to 100. Lisa wants to know at which number William lives.

She asks him: "Is your number larger than 50?"
William answers, but lies.
Upon this, Lisa asks: "Is your number a multiple of 4?"
William answers, but lies again.
Then Lisa asks: "Is your number a square?"
William answers truthfully.
Upon this, Lisa says: "I know your number if you tell me whether the first digit is a 3."
William answers, but now we don't know whether he lies or speaks the truth.

Thereupon, Lisa says at which number she thinks William lives, but (of course) she is wrong.

What is William's real house-number?

The fact that Lisa doesn't know whether or not the first digit is a 3 implies that William answered "no" to the first question.  Given that, the following scenario seems to work (using a little trial and error):

From Lisa's point of view:  The number is smaller than or equal to 50, a multiple of 4, and a perfect square.  16 and 36 both fit this criteria, and thus leads to her final statement.

The truth:  The number IS larger than 50, NOT a multiple of 4, and a perfect square.  Only House #81 fits the criteria.

William's final answer doesn't impact the final answer, but would determine Lisa's faulty answer.

Posted by Bryan on 2013-06-04 11:07:30