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 | + | 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 powers of 3 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 <math>28+9+3+1=41.</math> |
== See Also == | == See Also == |
Latest revision as of 19:16, 5 April 2020
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 powers of 3 in 9, so we need to add that to
and
and
, giving us
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 |