The House Where She Lives

Number Theory Level pending

My friend rang me up and invited me to her house. This is how she gave me the number of her house:

"I live in a long street where all the houses are in one row. All the houses in this street are numbered consecutively that is starting from one, two, three and so on. All the numbers on one side of my house add up to exactly the same as all the numbers on the other side of my house. I know there are more than 50 houses on that side of the street but not so many as 500".

What is my friend's house number?


The answer is 204.

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