Bob: I'm depressed. I moved here because the house number is special. The house numbers run consecutively from 1, and when you add up all the house numbers on my street, the sum is exactly the square of my house number. But a construction company is tearing down all the houses at one end of the street to build stores, and a second company is building more houses at the other end!
Sally: Don't worry, Bob. Your house number will be just as special when the construction is complete.
What is Bob's house number and how many houses are on the street?
Source: Original.
I get multiple solutions: b = Bob's number n = last present street number x = 1st street number after construction (has to be at low end) m = last number after new homes added x < b < n < m b^2 = n(n + 1) / 2 m = {sqrt[1 - 4(x - x^2 - 2b^2)] - 1} / 2 Keeping n < 10,000 I get 21 solutions: x b n m 18 35 49 52 196 204 288 348 595 1189 1681 1783 578 6930 9800 9817 755 6930 9800 9829 ......... 6194 6930 9800 11593 There are 18 with b=6930 and n=9800 : 21 cases for n < 10,000