Difference between revisions of "Random Problem"
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Revision as of 11:11, 30 January 2023
Contents
Easy Problem
The sum![\[\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\cdots+\frac{2021}{2022!}\]](http://latex.artofproblemsolving.com/7/2/6/726b88e230d5c0a0303ef6ca7177fa73b7eec900.png)
can be expressed as 
, where 
and 
are positive integers. What is 
?
Solution
???
Medium Problem
Show that there exist no finite decimals 
such that when its digits are rearranged to a different decimal 
, 
.
Solution
???
Hardish Problem
A cylinder is inscribed in a circular cone with base radius of 
and height of 
. What is the maximum possible volume of this cylinder is 
?
Solution
???
Hard Problem
A regular 
-gon is inscribed in a circle with radius 
. Let 
be the set of distances (not necessarily distinct) from the center of the circle to each side of the -gon, and 
be the set of distances (not necessarily distinct) from the center of the circle to each diagonal of the -gon. Let 
be the union of and . What is the sum of the squares of all of the elements in ?
Solution
???
