2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5
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Problem
is written on the blackboard. The sum of its digits is calculated. Then the sum of the
digits of the result is calculated and so on until we have a single digit. If 
, what
is this digit?
Solution
What you have to realize is that the sum of the digits of a number is the number 
. We can prove this right now.
\begin{equation}
\end{equation}
See also
| 2014 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNM-PNM Problems and Solutions | ||
