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Vandaag is het 26 September 2023

Address unknown - logic puzzle

Difficulty:

Rating: 3.2/5.0

Mr. House would like to visit his old friend Mr. Street, who is living in the main street of a small village. The main steet has 50 houses divided into two blocks and numbered from 1 to 20 and 21 to 50. Since Mr. House has forgotten the number, he asks it from a passer-by, who replies "Just try to guess it." Mr. House likes playing games and asks three questions:

1. In which block is it?
2. Is the number even?
3. Is it a square?

After Mr. House has received the answers, he says: "I'm still doubting, but if you'll tell me whether the digit 4 is in the number, I will know the answer!". Then Mr. House runs to the building in which he thinks his friend is living. He rings, a man opens the door and it turns out that he's wrong. The man starts laughing and tells Mr. House: "Your advisor is the biggest liar of the whole village. He never speaks the truth!". Mr. House thinks for a moment and says "Thanks, now I know the real address of Mr. Street".
What is the adress of Mr. Street?

Explanation

The address of Mr. Street is 14 Main Street.

There are 8 possible combinations of answers on the three questions:

 Case: Which block? Even? Square? Conclusion A first yes yes 4 or 16 B first yes no many C first no yes 1 or 9 D first no no many E second yes yes 36 F second yes no many G second no yes 25 or 49 H second no no many

Now it turns out that we only shoud consider cases A and G (because then the question about whether there is a 4 in the number makes sense). In case A the real number should be larger than 20, odd and no square. But then it would be impossible for Mr. House to know the correct number.
So we're left with case G. Mr. Street lives in the first block, with an even number, which is not a square. There is only one number which has a 4 in it, number 14.
Mr. House was told by the passer-by to go to number 25. But Mr. Street lives on 14 Main Street.