Finding Address !
It was Iftar Party at Lucknow that Mr. David me Mr. Naqvi. They became friends and exchanged their phone numbers. After a few days, Mr. David rang up and invited Mr. Naqvi for New Year Party at this house and gave him his house number as follows:
“I live in a long street. Numbered on the side of my house are houses one,two, three, and so on. All the numbers on one side of my house add up to exactly the same as all numbers on other side of my house. I know there are more than thirty houses on that side of the street, but not so many as 50.”
With this information Mr. Naqvi was able to find Mr. David’s house number. Can you also find?
The answer is 35.
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1 solution
Let there be n houses on the side of street. The problem then states 30 < n < 50.
Let K be the house number where the party is.
Sum of all house numbers on left of K = (K-1)(1 + K-1)/2
Sum of all house numbers on right of K = (n - K)(K + 1 + N)/2
Equating both and solving gives: K = sqrt[n(n+1)/2].
The only value for n in the range 30 < n < 50 which gives integer K is n =49. K =35.