House Number? (1)

Number Theory Level 3

Inspired by a similar problem on this site.

I live on a street full of houses. They run from 1 to 478. After a series of events I have now forgotten which house I live at. I need you to work out which house number I live at from the following clues that I have retained:

  1. I live on the even side of the street (all houses on my side of the street are even numbered).

  2. My house is located above (in numerical value) house number 418 (my friend Bob lives there).

  3. The sum of the even house numbers between Bob's house and my house (not including his or mine), is equal to the sum of even house numbers after my house until the end of the street at 478.

Can you help me find where I live? Type the house number as the answer.


Problem Loading...

Note Loading...

Set Loading...