1998 AHSME Problem 24

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 different memorable telephone numbers is

\mathrm{(A) \ } 19,810 \qquad \mathrm{(B) \ } 19,910 \qquad \mathrm{(C) \ } 19,990 \qquad \mathrm{(D) \ } 20,000 \qquad \mathrm{(E) \ } 20,100

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.