# 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

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