2006 Cyprus MO/Lyceum/Problem 13

Revision as of 19:23, 17 October 2007 by Azjps (talk | contribs) (sol)

Problem

The sum of the digits of the number $10^{2006}-2006$ is

A. $18006$

B. $20060$

C. $2006$

D. $18047$

E. None of these

Solution

$10^{2006}$ is a $1$ followed by 2006 $0$s; when we subtract, we will get something approximately close to 2006 $9$s. The last four digits are $10000 - 2006 = 7994$, and so we have 2002 $9$s followed by $7994$. The sum of these is $2002 \cdot 9 + 7 + 9 + 9 + 4 = 18047 \Longrightarrow \mathrm{(D)}$

See also

2006 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 12
Followed by
Problem 14
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