AoPS Academy
+1 w
sigmas = 
looksmaxxers, and 
looksmaxxers = 
skibdis, how many skibidis are in a sigma? Express your answer as a common fraction
such that 
is a perfect square
concentric circles with radii 
, , and are on a dartboard, where hitting the center circle is points, hitting the region outside the center circle but within the circle with radius is worth points, and hitting the outermost region is worth point. If Mary hits the dartboard at a random location 
of the time and John hits the dartboard randomly 
of the time, what is the probability, that after throw, John has more points than Mary?
concentric circles with radii , , and are on a dartboard, where hitting the center circle is points, hitting the region outside the center circle but within the circle with radius is worth points, and hitting the outermost region is worth point. If Mary hits the dartboard at a random location of the time and John hits the dartboard randomly of the time, what is the probability, that after throw, John has more points than Mary?
because 
which is a perfect square
both fail since 
are not perfect squares. We see that 
works since 
.
has 
,
,
.
?
to get 
.![$\pi(\pi[\pi(1, 2), \pi(3, 4)], \pi[\pi(5, 6), \pi(7, 8)])$](http://latex.artofproblemsolving.com/0/4/a/04a9be80e0c7395b09a61906540eff9cd5a96ce8.png)
?
kind of approximates the average of 
and 
.
is a little closer to ![$\pi(\pi[\pi(1, 2), \pi(3, 4)], \pi[\pi(5, 6), \pi(7, 8)]) \approx \pi(\pi[1.5, 3.5], \pi[5.5, 7.5]) \approx \pi(2.5, 6.5) \approx 4.5$](http://latex.artofproblemsolving.com/0/6/a/06ac4d3a375a6723e3834045764f2c5a7a43f637.png)
,
than to 
as the 
makes the expression closer to 
