# Moving House Puzzle - Solution

## The Puzzle:

A man who had lived at the highest-numbered address on his street moved to another house on the same street.

He noted that the sum of all the addresses below his new address was the same as the sum of all the addresses above his new address. (Every numbered address on the street is used.)

He had owned some beautiful brass house numbers and was pleased to discover that he did not have to purchase any new ones. For his new house, he used all of the brass numbers from his previous house.

What is his new address?

He noted that the sum of all the addresses below his new address was the same as the sum of all the addresses above his new address. (Every numbered address on the street is used.)

He had owned some beautiful brass house numbers and was pleased to discover that he did not have to purchase any new ones. For his new house, he used all of the brass numbers from his previous house.

What is his new address?

## Our Solution:

Solution by Zach Cooper:

Old Address: 1681

New Address: 1189

The summation of integers 1 through 1188 is equal to the summation of integers 1190 through 1681. Additionally, the person can reuse their number labels since they both have 1, 1, and 8, and you could flip the 6 upside-down to be the 9.

Old Address: 1681

New Address: 1189

The summation of integers 1 through 1188 is equal to the summation of integers 1190 through 1681. Additionally, the person can reuse their number labels since they both have 1, 1, and 8, and you could flip the 6 upside-down to be the 9.

Puzzle Author: Mitchell Marcus