perplexus.info :: Logic : William's house-number

William's house-number (Posted on 2013-06-04)

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?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

a d1 answer

| Comment 3 of 5 |

81.

It had to be a square number, since Lisa hesitated between 2 possible choices.

The two sets under 50 and 50+ were (9,16,25,36,49) and(64,81,100).

Lisa considered a wrong pair (16,36) while,being led astray by wrong answers, missed a number which is over 50 and is not a multiple of 4.

WILLIAM's 3 answers were no,yes,yes and Lisa's choice was either 36 (yes for the "3" digit ) or 16()case of "no").

Edited on June 4, 2013, 1:30 pm

Posted by Ady TZIDON on 2013-06-04 13:05:03

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