Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 1"
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== Solution == | == Solution == | ||
| − | Let <math>\lfloor x \rfloor</math> indicate the largest integer less than or equal to x. To solve this problem, we simply need to find the powers of 3 that go into 85. Thus we get <math>\lfloor \frac{85}{3} \rfloor</math>. But that doesn't count the 2 3's in 9, so we need to add that to <math>\lfloor \frac{85}{9}</math> and <math>\lfloor \frac{85}{27} \rfloor</math> and <math>\lfloor \frac{85}{81} \rfloor</math>, giving us 41. | + | Let <math>\lfloor x \rfloor</math> indicate the largest integer less than or equal to x. To solve this problem, we simply need to find the powers of 3 that go into 85. Thus we get <math>\lfloor \frac{85}{3} \rfloor</math>. But that doesn't count the 2 3's in 9, so we need to add that to <math>\lfloor \frac{85}{9} \rfloor</math> and <math>\lfloor \frac{85}{27} \rfloor</math> and <math>\lfloor \frac{85}{81} \rfloor</math>, giving us 41. |
== See Also == | == See Also == | ||
Revision as of 14:22, 13 August 2015
Problem
The largest integer 
so that 
evenly divides 
is 
. Determine the largest integer so that evenly divides 
.
Solution
Let 
indicate the largest integer less than or equal to x. To solve this problem, we simply need to find the powers of 3 that go into 85. Thus we get 
. But that doesn't count the 2 3's in 9, so we need to add that to 
and 
and 
, giving us 41.
See Also
| 2011 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
