## Srinivasa’s street brainteaser

By David Shaw, 18 May 2022

**Difficulty: Extreme!**

Srinivasa lives in a house on a short street, with houses on one side. The houses are numbered 1, 2, 3 and so on. He was practicing his addition when he noticed something strange.

On Monday, he turned right when he walked out the front door in the morning and added up all the house numbers he passed. On Tuesday, he turned left instead and added up the house numbers on the other end of the street. Surprisingly, the totals were the same!

Srinivasa’s street is not more than 10 houses long. How many houses are there on Srinivasa’s street?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

The street isn’t 3 houses long. Srinivasa didn’t count his own house in either total!

## Brainteaser answer

A good first step for this brainteaser is to draw a number line to act as a street. You only need to use the numbers 1 to 10, because we know his street is at most 10 houses long. Then you can try putting Srinivasa’s house at different points and see if you can make the 2 sides add up to the same total.

Srinivasa can’t live at number 2 or 3 because there aren’t enough small numbers to balance one house bigger than his house number.

Living at house 4 or 5 looks more promising, but doesn’t quite work.

If Srinivasa lives at house 6, the lower side of the street adds up to 5 + 4 + 3 + 2 + 1 = 15.

Going the other way, the next house is 7, and then 8. And 7 + 8 = 15, exactly the total we’re looking for!

So Srinivasa lives at number 6 on a street with 8 houses.

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