If only the positive integers from 1 through 49, inclusive, are written on a piece of paper, what is the sum of all the digits that are written on the paper?

Lightning
Aug 26, 2018

#1**+3 **

\(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(1\)\(0\) |

\(1\)\(1\) | \(1\)\(2\) | \(1\)\(3\) | \(1\)\(4\) | \(1\)\(5\) | \(1\)\(6\) | \(1\)\(7\) | \(1\)\(8\) | \(1\)\(9\) | \(2\)\(0\) |

\(2\)\(1\) | \(2\)\(2\) | \(2\)\(3\) | \(2\)\(4\) | \(2\)\(5\) | \(2\)\(6\) | \(2\)\(7\) | \(2\)\(8\) | \(2\)\(9\) | \(3\)\(0\) |

\(3\)\(1\) | \(3\)\(2\) | \(3\)\(3\) | \(3\)\(4\) | \(3\)\(5\) | \(3\)\(6\) | \(3\)\(7\) | \(3\)\(8\) | \(3\)\(9\) | \(4\)\(0\) |

\(4\)\(1\) | \(4\)\(2\) | \(4\)\(3\) | \(4\)\(4\) | \(4\)\(5\) | \(4\)\(6\) | \(4\)\(7\) | \(4\)\(8\) | \(4\)\(9\) |

By the chart, you can see that there are:

Fifteen \(1\)'s

Fifteen \(2\)'s

Fifteen \(3\)'s

Fifteen \(4\)'s

Five \(5\)'s

Five \(6\)'s

Five \(7\)'s

Five \(8\)'s

Five \(9\)'s and

Four \(0\)'s (Of course, the zero's would not matter, because they are asking for the sum).

So we are trying to find \(s\), the sum of the digits. We can get the equation \(s = 15(1) + 15(2) + 15(3) + 15(4) + 5(5) + 5(6) + 5(7) + 5(8) + 5(9) \), which is equal to \(s = 15 + 30 + 45 + 60 + 25 + 30 + 35 + 40 + 45\), which we can finally get \(s = 325\)

- Daisy

dierdurst
Aug 26, 2018