,![\[
1^2 + 2^2 + 3^2 + \ldots + k^2 = \frac{k(k + 1)(2k + 1)}{6}
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Find the smallest positive integer 
is divisible by 200.
,
,
.![\[
a^2 + b^2 + c^2 + 4abc < \frac{1}{2}.
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are positive real number such that 
.
, where 
always occurs at 
be a positive integer. Find the smallest value of 
is divisible by 
.
and 
Prove that
?
numebr on his list? Write its last two digits as your answer.
grid of square tiles. Robert chooses four of these squares uniformly at random. The probability that the centers of these four squares form a square themselves is 
where 
are coprime naturals. Write the largest 
digit odd factor of 
.
.
vertices of the face opposite to it. Find the integer closest to 
are distinct numbers in AP such that 
are also in AP. Find the smallest possible value of 
(in degrees).
that satisfy 
Y by
Problem 1:
Three circles with radius
are tangent to each other and internally tangent to a circle with radius 
Find 
Problem 2:
A circle with radius is centered at the centroid of an equilateral triangle with side length Three other circles with radius are internally tangent to exactly two sides of the equilateral triangle, and to the circle at the centroid of the equilateral triangle. Find
Three circles with radius
are tangent to each other and internally tangent to a circle with radius 
Find 
Problem 2:
A circle with radius
is centered at the centroid of an equilateral triangle with side length Three other circles with radius are internally tangent to exactly two sides of the equilateral triangle, and to the circle at the centroid of the equilateral triangle. Find This post has been edited 2 times. Last edited by ReticulatedPython, Mar 14, 2025, 5:22 PM
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