Correct Address Identified !
How pointed towards the wrong one?
Since Mr. House was able to run at one house after answers of passer-by, he must have got clear clues from that.
3. Is it square ?
First thing is sure that, the number must not be a non-square otherwise Mr.House wouldn't be sure as there are plenty of non-square numbers between 1 to 50. So it must be either 4,9,16,25,36,49. (1 is omitted for a reason)
-----------------------------------------------------------------------------------------
1. In which block is it?
Two possible answers here & 2 possible conclusions.
Block 1 : 4,9,16
Block 2 : 25,36,49
------------------------------------------------------------------------------------------
2. Is the number even ?
Now had passer-by answered Block 1 in 1st question & odd now then Mr. House would have come to know one exact number 9 (that's why 1 omitted here).
Or had he answered Block 2 in 1st question & even now then also Mr. House would have 1 number i.e. 36.
So in both cases, Mr. House would have got 1 fixed number with no point in asking extra question.
That means the passer-by must have told following answers & their possible conclusions are-
Block 1 : Even : Square : 4,16
Block 2 : Odd : Square : 25,49
-----------------------------------------------------------------------------------------
Now, this made Mr. House unsure about exact number & hence he asks further if 4 is part of that number or not? Now let's take a look at possible combinations & results.
1. YES : Block 1 : Even : Square : 4
2. NO : Block 1 : Even : Square : 16
3. YES : Block 2 : Odd : Square : 49
4. NO : Block 2 : Odd : Square : 25
------------------------------------------------------------------------------------------
Now depending on 4 answers, Mr. House must have run to either 4, 16 , 49 or 25. Let's remind that all these were wrong & Mr. House need to go back & apply clues with passer-by's answers inverted. If we assume Mr. House visited 4 but with wrong clues. If clues were correct then,
1. NO : Block 2 : Odd : Non-Square : 21,23,27,29,31,33,35,37,39
Like away, for other cases,
2. YES : Block 2 : Odd : Non-Square : 41,43,44,45,47
3. NO : Block 1 : Even : Non-Square : 2,6,8,10,12,16,18
4. YES : Block 1 : Even : Non-Square : 14 only (4 is square of 2).
Now in first attempt Mr.House visited wrong house but in second found the correct one. Had he visited 4,16,49 then he would have more than 1 number after applying inverted answers by passer-by's). Since he was sure with the correct number at the end, he must have visited 25 in first attempt & after applying modified clues he visited 14.
