Difference between revisions of "2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5"
Mathwizard07 (talk | contribs) (→Solution) |
Mathwizard07 (talk | contribs) |
||
Line 7: | Line 7: | ||
== Solution == | == Solution == | ||
What you have to realize is that the sum of the digits of a number is the number <math>\pmod{9}</math>. We can prove this right now. | What you have to realize is that the sum of the digits of a number is the number <math>\pmod{9}</math>. We can prove this right now. | ||
− | + | \begin{equation} | |
− | + | \end{equation} | |
− | |||
− | |||
− | |||
== See also == | == See also == | ||
{{UNM-PNM Math Contest box|year=2014|n=II|num-b=4|num-a=6}} | {{UNM-PNM Math Contest box|year=2014|n=II|num-b=4|num-a=6}} | ||
− | [[Category:Intermediate | + | [[Category:Intermediate Algebra Problems]] |
Revision as of 02:05, 17 March 2019
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 |