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new math puzzle

milagros317

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Time for a new math puzzle.

Alice lives on the south side of a long street.
On the south side, all of the houses have even numbers: 2, 4, 6, ...
Alice's house number has three digits.

Alice, who is compulsive about numbers, says, "The sum of the even house numbers on this street below mine is exactly equal to the sum of the even house numbers on this street above mine! Moreover, this common sum is just one less than my zip code."

a) What is Alice's house number?
b) What is the highest even house number on this street?
c) Where does Alice live?

Solution will be posted in one week if nobody solves it.
 
Alice's house number is at least.... (and the left side of my flabby brain just shut down.)

But really, thank you for attempting to provide us with helpful mental exercises! They are much needed! :atom:
 
Last edited:
There would be infinitely many solutions without the condition in italics:
Alice's house number has three digits.

The smallest non-trivial solution is:

Alice's house number is 12.
The highest even house number is 16.
Note that 2+4+6+8+10 = 30 = 14+16.

The unique solution that satisfies the condition in italics is:

Alice's house number is 408.
The highest even house number is 576.
Note that 2+4+6+...+406 = 41,412 = 410+412+414+...+576.

Finally, 41412+1 = 41413 and that zip code shows that Alice lives in Crockett, Kentucky.
 
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