# 1998 AHSME Problem 24

**Discrete Mathematics**Level 2

Call a 7-digit telephone number \(d_1d_2d_3-d_4d_5d_6d_7\) memorable if the prefix sequence \(d_1d_2d_3\) is exactly the same as either of the sequences \(d_4d_5d_6\) or \(d_5d_6d_7\) (possibly both). Assuming that each \(d_i\) can be any of the ten decimal digits \(0,1,2, \ldots 9\), the number of difference memorable telephone numbers is