rows and 
columns, with 
.
,
rows of this grid together occupy at least 
s
r
t
and 
has the property for every positive integer 
,
term is greater than the mean of the first 
terms, and the sum of its first 
be the number of such sequences satisfying 
.
.
has side length 
lies on segment 
such that line 
is perpendicular to line 
.
,
,
.
and 
satisfy 
,
,
.
is equal to 
,
be a triangle. Point 
lies on side 
,
lies on side 
,
lies on side 
such that 
,
,
.
be the foot of the altitude from 
to 
,
,![$[AQPR] = \tfrac{3}{7} \cdot [ABC]$](http://latex.artofproblemsolving.com/e/f/1/ef1f89d7ee2b45faac7265d8e2777ba3918ae16e.png)
,
can be expressed as 
and tells Bob that the three resulting remainders are 
,
,
satisfying the system of equations 
The value of 
can be expressed as 
,
and 
are positive integers such that 
.
and 
inclusive. We say a sequence 
in 
,
that are at least 
is 
.
,
denote the value of the binary number obtained by reading the binary representation of 
has at least ten positive integer solutions 
such that 
and 
for 
.
.
such that 
and 
is a multiple of 
.
,
,
,
For example, 
.
functions 
whose domain and range are the set 
,
for all 
.
be an acute triangle with 
.
and 
intersect at point 
.
be the feet of the perpendicular from 
.
and 
lie on segments 
and 
,
.![\[
\angle KAL = \frac{1}{2} \angle BAC.
\]](http://latex.artofproblemsolving.com/f/a/d/fad437704b2dcdc39ce04b23f860d26b764fd3a2.png)
ad 
be two circles intersecting at 
The tangent like closer to 
and 
and 
find 
then we could just use the ratio us between the side lengths of these triangles to find 
and 
where 
is the digit sum of 
,
Y by Yrock, Exponent11, PikaPika999
Summary of the problem: When using exit() (or quit()) in the Python windows on AoPS the "Description" and "To fix" options show up as "undefined"
Page URL: N/A
Steps to reproduce:
1. Use the AoPS Python module to execute the exit() or quit() functions in a program. (try running the sample program)
Expected behavior: The "Description" and "To fix" sections give a description of SystemExit
Frequency: Always
Operating system(s): Windows 11 Home
Browser(s), including version: Microsoft Edge 130.0.2849.46
Additional information: N/A
Page URL: N/A
Steps to reproduce:
1. Use the AoPS Python module to execute the exit() or quit() functions in a program. (try running the sample program)
Expected behavior: The "Description" and "To fix" sections give a description of SystemExit
Frequency: Always
Operating system(s): Windows 11 Home
Browser(s), including version: Microsoft Edge 130.0.2849.46
Additional information: N/A
Attachments:
This post has been edited 2 times. Last edited by SoaringHigh, Oct 22, 2024, 2:11 PM
