[/quote]
,
table filled with natural numbers, we say it is a divisor table if:
-
,
-
,
for every 
.
is given. Determine the smallest natural number 
,
be a triangle inscribed in circle 
such that points 
are fixed, while 
moves on major arc 
of 
and 
to 
.
intersects 
and 
at 
and 
,
is tangent to a fixed circle whose radius is half the radius of 
and 
be the circumcenter, centroid and symmedian point of 
respectively. 
Show that the 
falls on 
such that if 
,
by 
also belongs to 
.
,
,
in the plane, such that the area of convex hull of 
is at most 
denotes the image of 
be positive integers such that 
is a square. Prove that 
is not prime.
with parallel sides 
and 
,
on line 
outside segment 
inside segment 
such that 
.
the point of intersection of 
,
the point of intersection of 
be the midpoint of segment 
if and only if 
.
such that 
is the square of an integer.
prove that
satisfy 
.
Given this fact, determine the exact value of 
(Source: Mandelbrot)
wooden cube is painted on all six faces, then cut into 27 unit cubes. One unit cube is randomly selected and rolled. After it is rolled, 
out of the 
faces are visible. What is the probability that exactly one of the five visible faces is painted? (Source: MATHCOUNTS)
Y by aidan0626, e_is_2.71828, Exponent11, PikaPika999
i don't even know if this is solvable
Prove that there are finite/infinite powers of 2 where all the digits are also powers of 2. (For example,
and 
are numbers that work, but 
and 
don't work.)
Prove that there are finite/infinite powers of 2 where all the digits are also powers of 2. (For example,
and 
are numbers that work, but 
and 
don't work.)This post has been edited 1 time. Last edited by ceilingfan404, Apr 20, 2025, 7:55 PM
)
-
.
,
,
.
.
for some 
,
,
.
always have a digit equal to 
would be broken down into 
and since a, b,c are powers of 2, you could just look at the 5s?) idk how to continue though.
,
in base 
?
