Difference between revisions of "Random Problem"
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Revision as of 12:11, 30 January 2023
Contents
Easy Problem
The sumcan 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
?? ?