## House Numbers

Ross live's on a road with \(N\) houses numbered from \(1\) to \(N\). Amazingly, the sum of all the house numbers before his house is equal to the sum of all the house numbers after his house. So for example, it is possible that \(N=8\) if Ross lived in house number \(6\) because \(1+2+3+4+5 = 7+8\).

Part A | If \(N>10\), what is the smallest possible value of \(N\)? | |
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Part B | If \(N>10000\) what is the smallest possible value of \(N\)? | |

Part C | If \(N>10^9\) what is the smallest possible value of \(N\)? |