house number puzzle

[milagros317]

Problem A

You live on a long street that runs north/south. Like most streets, the odd numbered addresses are on one side of the
street and the even numbered addresses are on the other side. Your house has an odd numbered address.

On your side of the street the southern most house is number 1, then come numbers 3, 5, 7, and so on until the northern
most house which has the highest number. There are more than 100 houses on your side of the street but fewer than
1,000 houses.

Incredibly, looking at only your side of the street, the sum of the numbers of all the houses south of your house is
exactly equal to the sum of the numbers of all the houses north of your house.

What is number of your house? What is the number of the highest numbered house on your side of the street?



Problem B

You have moved and now live on a different street in a different city.

You live on a long street that runs north/south. Like most streets, the odd numbered addresses are on one side of the
street and the even numbered addresses are on the other side. Your house has an even numbered address.

On your side of the street the southern most house is number 2, then come numbers 4, 6, 8, and so on until the northern
most house which has the highest number. There are more than 100 houses on your side of the street but fewer than
1,000 houses.

Incredibly, looking at only your side of the street, the sum of the numbers of all the houses south of your house is
exactly equal to the sum of the numbers of all the houses north of your house.

What is number of your house? What is the number of the highest numbered house on your side of the street?




If nobody solves this within a week, then I will post both answers.

 

[milagros317]

Solution to Problem A:

Your house number is 239. The highest numbered house on your side of the street is 337.
1 + 3 + 5 + ... + 237 = 14,161 and 241 + 243 + 245 + ... + 337 = 14,161



Solution to Problem B:

Your house number is 408. The highest numbered house on your side of the street is 576.
2 + 4 + 6 + ... + 406 = 41,412 and 410 + 412 + 414 + ... + 576 = 41,412


Note to both solutions:
If the restriction "There are more than 100 houses on your side of the street but fewer than
1,000 houses," is removed, then there are infinitely many solutions to both problems.

 

[rdhd]

That's one long street......

 

[milagros317]

That's one long street......

Street numbers on Broadway, here in Manhattan, go over 5000.
Down there in Atlanta, house numbers on Peachtree Street go over 1000.

 

[rdhd]

Yeh, until the street name abruptly change to something else. Would have been nice to have Excel to try to solve this one, but a few months ago my computer decided to reboot Windows, and thus wiped the program (and Word, etc.) from my computer. Such is my life. But, keep us thinking, Milagros.

 

[milagros317]

Yes, an Excel spread sheet could solve it by brute force, but not find the infinite family of solutions.