add-on such as 
.
,
.
essentially killed the problem I had in mind. With this breakthrough, I hid the true meaning of the question and eventually came up with 
is a bad problem because although the idea of geometric sums is easy, computing 
is not.
such that 
.![\[\sqrt[4]{(1-a^4)(1-b^4)(1-c^4)(1-d^4)}\geq 255\cdot abcd.\]](http://latex.artofproblemsolving.com/d/e/6/de61611f628ea796c706d05941d7ee9b3fc22916.png)
to be polynomial like if 
for all 
.
of positive integers is called Mahismatian if there's a constant 
such that 
for all 
.
is Mahismatian then there exists fixed constants 
with 
for all 
is given in the plane, let 
be the set of points which lie strictly inside it. Also let 
be the set of circles in the plane. For a point 
,
be the reflection of 
in sides 
respectively. Define a function 
such that 
is the circumcircle of 
.
injective?
,
,
be a positive integer. and 
denote the number of solutions to 
,
is allowed to vary on the set of positive integers
for all 
infintiely many often.
.
such that 
be the foot of altitudes from 
onto the opposite sides respectively and 
the orthocentre. Reflect 
to obtain 
.
such that 
is the incentre of 
.
and 
be the midpoints of 
and 
respectively, then show that 
are collinear.
be a positive integer. There're 
roads in Mahismati, no three roads are concurrent and no two roads are parallel (so each two of them intersect). Number all possible 
angles formed by intersection points with 
in any order.
if he goes through 
,
(or vice versa). Katappa colors two numbers 
with 
with the same color iff there's a path traced by Baahubali which touches the angles numbered 
colors will be used by Katappa to color all the numbers?
: In the picture attached below, total 
colors will be used to color the numbers in each set with same color 
.
will be colored with the same color because the red path traced by Baahubali touches the angles 
.
![\[\text{Average score of each problem (out of 17)}.\]](http://latex.artofproblemsolving.com/a/a/d/aada9166e7a409b02f8f7355bb9e60800298c4b5.png)
specifies the greatest common divisor of 
PM submissions to me
[rule]
.
.
[center]Honor Roll[/center]
[center]Honor Roll[/center]
Y by NJOY, PCChess, jeteagle, kevinmathz, mathicorn, amar_04, samuel, vsamc, SenorIncongito, andyxpandy99, IMOTC, Math-wiz, Orestis_Lignos, Jerry122805, Aathreyakadambi, Ish_Sahh, mathtiger6, cw357, Awesome_guy, spike2015, rg_ryse, A-Thought-Of-God, mathleticguyyy, OlympusHero, Lcz, chelseafcc, Pleaseletmewin, math31415926535, v4913, bowenying24, DAWAE, CT17, superagh, bobthegod78, RJ5303707, myh2910, megarnie, HockeyMaster85, Sedro
What's up AoPS Community?
We, The OTSS Committee, are back! With Aathreyakadambi, AIME12345, ARMLlegend, Awesome_guy, AwesomeYRY, azduncan, DeToasty3, Emathmaster, Ish_Sahh, ivyzheng, jeteagle, kevinmathz, MathCounts145, NJOY, Orestis_Lignos, PCChess, reaganchoi, rqhu, VulcanForge,
zhao_andrew on board, we present you the
![[asy]
usepackage("fourier");
usepackage("xcolor");
defaultpen(font("T1","fut\textfamilyextension","m","n"));
defaultpen(fontsize(18.05pt));
defaultpen(1.1);
size(3.05cm);
pair A,B,C,D,E;
A=(-0.1,1);
B=(-0.10,0);
C=(0.45,1);
D=(1.2,1);
E=(0.825,0);
draw(ellipse((-0.1,0.5),0.375,0.5),heavycyan+linewidth(3));
draw(C--D,blue+linewidth(3));
draw(((0.825,1)--E),blue+linewidth(3));
dot(A,blue);
dot(B,blue);
dot(C,heavycyan);
dot(D,heavycyan);
dot(E,heavycyan);
pair F,G,H,I;
F=(1.5, 0.75);
G=(2.1, 1);
H=(1.5, 0);
I=(2.1, 0.25);
draw(F--G,heavycyan+linewidth(3));
draw(F--I,heavycyan+linewidth(3));
draw(H--I,heavycyan+linewidth(3));
dot(F,blue);
dot(G,blue);
dot(H,blue);
dot(I,blue);
pair J,K,L,M;
J=(2.4, 0.75);
K=(3, 1);
L=(2.4, 0);
M=(3, 0.25);
draw(J--K,blue+linewidth(3));
draw(J--M,blue+linewidth(3));
draw(L--M,blue+linewidth(3));
dot(J,heavycyan);
dot(K,heavycyan);
dot(L,heavycyan);
dot(M,heavycyan);
label("\textbf{\color{blue}O}\color[HTML]{3D85C6}nline \textbf{\color{blue} T}est \textbf{\color{blue} S}nowy \textbf{\color{blue} S}eries",(-0.455,-0.1)--(3.02,-0.1),S);
[/asy]](//latex.artofproblemsolving.com/5/d/0/5d073191559462009c5102c80741b36566bcfcde.png)
This series of contests will once again be designed for people to get more familiar and obtain extra practice with the MAA series test, i.e. AMC, AIME, and USA(J)MO, and we have again called it the Test Mathematics Competitions (TMC), the Online Test Invitational Examination (OTIE), and the Online Test Junior Mathematical Olympiad (OTJMO), respectively. Please note that, unlike the MAA Tests, you do not have to qualify for a competition to take it, and you do not have to be under a certain age to take any of the tests.
Important Updates and Credits:
Schedule:
(Release time of the tests is 12 (
5 minutes) AM EsT on the dates and Deadline time is 10 PM EST on the mentioned dates.)
Registration:
To sign-up, use , noting that
Submissions:
Aftermath (haha get it):
After you submit a contest, you will be added to our private discussion forum here. After the window for each contest officially closes, we will create threads of the problems in the Season 2 Discussion Forum here. Anonymous feedback forms are presented here; but we will only private message you the password after you submit a test. Please do not publicly discuss the problems on the tests until we have posted at least one problem to the forum or posted the answer key.
Message about Trolling:
Remember that trolling or intentionally sabotaging this thread will demonstrate a lack of maturity in you and reflect negatively. Being able to take this test is our gift to you and the AoPS community, but we do not have to give it. So, please do not try to sabotage our thread. It will only waste the time of AoPS mods and admins, along with wasting your time. If you have any questions or concerns, the best way to tell us is by private message.
Finally... Stay safe and inflate the Math curve!
The OTSS Committee
Contest Info and Test URLs:
We, The OTSS Committee, are back! With Aathreyakadambi, AIME12345, ARMLlegend, Awesome_guy, AwesomeYRY, azduncan, DeToasty3, Emathmaster, Ish_Sahh, ivyzheng, jeteagle, kevinmathz, MathCounts145, NJOY, Orestis_Lignos, PCChess, reaganchoi, rqhu, VulcanForge,
zhao_andrew on board, we present you the
![[asy]
usepackage("fourier");
usepackage("xcolor");
defaultpen(font("T1","fut\textfamilyextension","m","n"));
defaultpen(fontsize(18.05pt));
defaultpen(1.1);
size(3.05cm);
pair A,B,C,D,E;
A=(-0.1,1);
B=(-0.10,0);
C=(0.45,1);
D=(1.2,1);
E=(0.825,0);
draw(ellipse((-0.1,0.5),0.375,0.5),heavycyan+linewidth(3));
draw(C--D,blue+linewidth(3));
draw(((0.825,1)--E),blue+linewidth(3));
dot(A,blue);
dot(B,blue);
dot(C,heavycyan);
dot(D,heavycyan);
dot(E,heavycyan);
pair F,G,H,I;
F=(1.5, 0.75);
G=(2.1, 1);
H=(1.5, 0);
I=(2.1, 0.25);
draw(F--G,heavycyan+linewidth(3));
draw(F--I,heavycyan+linewidth(3));
draw(H--I,heavycyan+linewidth(3));
dot(F,blue);
dot(G,blue);
dot(H,blue);
dot(I,blue);
pair J,K,L,M;
J=(2.4, 0.75);
K=(3, 1);
L=(2.4, 0);
M=(3, 0.25);
draw(J--K,blue+linewidth(3));
draw(J--M,blue+linewidth(3));
draw(L--M,blue+linewidth(3));
dot(J,heavycyan);
dot(K,heavycyan);
dot(L,heavycyan);
dot(M,heavycyan);
label("\textbf{\color{blue}O}\color[HTML]{3D85C6}nline \textbf{\color{blue} T}est \textbf{\color{blue} S}nowy \textbf{\color{blue} S}eries",(-0.455,-0.1)--(3.02,-0.1),S);
[/asy]](http://latex.artofproblemsolving.com/5/d/0/5d073191559462009c5102c80741b36566bcfcde.png)
This series of contests will once again be designed for people to get more familiar and obtain extra practice with the MAA series test, i.e. AMC, AIME, and USA(J)MO, and we have again called it the Test Mathematics Competitions (TMC), the Online Test Invitational Examination (OTIE), and the Online Test Junior Mathematical Olympiad (OTJMO), respectively. Please note that, unlike the MAA Tests, you do not have to qualify for a competition to take it, and you do not have to be under a certain age to take any of the tests.
Important Updates and Credits:
- Thank you for participating in OTSS this season and good luck on the actual AMCs!
- All the tests are ready; the TMC 10/12 has been test-solved by ASawesome, ASweatyAsianBoie, Bacon2387, karate7800, nikenissan, and smartatmath, the OTIE has been test-solved by ASawesome, Bacon2387, bobthefam, smartatmath, and twinbrian, and the OTJMO has been test-solved by a1267ab, CantonMathGuy, pieater314159, and tastymath75025. Thanks to all of you for giving us valuable feedback and suggestions on improvement!
- A special thanks goes to both Mathotsav and Supercali for making valuable contributions to our tests!
- For any questions or comments, you may either email us at otss.contactus@gmail.com or you can send an AoPS Private Message (obviously, when signed in) to Emathmaster and kevinmathz.
- Our website is https://online-test-seasonal-series.github.io. This website has our archives, news, current members and some handouts we will be working on.
Schedule:
(Release time of the tests is 12 (
5 minutes) AM EsT on the dates and Deadline time is 10 PM EST on the mentioned dates.)
Registration:
To sign-up, use , noting that
- It is recommended to use the bbcode (i.e. the "list") to add your name to the sign-ups.
- The sign-ups are a means to get an estimate of the number of submissions we are going to receive, but it is not required by any means, and will have no impact on your result.
- You'll receive notifications in the "My Topics Feed" whenever something happens in this thread.
Submissions:
- Submissions for TMC and OTIE will be via private message to DeToasty3, Emathmaster, jeteagle, and kevinmathz, who will add other members of the committee to the private message.
- For the OTJMO, please consult the Instructions document (located in the "Contest Info and Test URLs" section of this post) for information on how to submit.
- Grading will be automatic via our computer code; however, this does not mean we will be able to return scores immediately. Thus, in order for us to grade your submissions for the TMC and OTIE, please submit your solutions in one line.
- If you wish to leave anything blank for the TMC, please write
. For example, this would be a valid submission: 0BCDE A0CDE AB0DE ABC0E ABCD0 - If you wish to leave anything blank for the OTIE, please write
. For example, if the answers to their problems were their numbers, with problem 11 blank, this would be a valid submission:
001 002 003 004 005 006 007 008 009 010 BBB 012 013 014 015
Aftermath (haha get it):
After you submit a contest, you will be added to our private discussion forum here. After the window for each contest officially closes, we will create threads of the problems in the Season 2 Discussion Forum here. Anonymous feedback forms are presented here; but we will only private message you the password after you submit a test. Please do not publicly discuss the problems on the tests until we have posted at least one problem to the forum or posted the answer key.
Message about Trolling:
Remember that trolling or intentionally sabotaging this thread will demonstrate a lack of maturity in you and reflect negatively. Being able to take this test is our gift to you and the AoPS community, but we do not have to give it. So, please do not try to sabotage our thread. It will only waste the time of AoPS mods and admins, along with wasting your time. If you have any questions or concerns, the best way to tell us is by private message.
Finally... Stay safe and inflate the Math curve!
The OTSS Committee
Contest Info and Test URLs:
- OTJMO: (Instructions) (Day 1) (Day 2) (Solutions)
- TMC 10: (Paper) (Solutions)
- TMC 12: (Paper) (Solutions)
- OTIE: (Paper) (Solutions)
- Cutoff: 222.5
- Cutoff: 229
![[asy]
unitsize(1cm);
real x, y;
real[] hist = {0, 0, 1, 1, 3, 1, 2, 5, 4, 6, 5, 1, 1, 1, 0, 0};
x = 0.75;
y = 0.15;
draw((x,0)--(16*x,0));
for(int i = 0; i < 16; ++i) {
draw((i*x,0)--(i*x,hist[i]*y*5)--((i + 1)*x,hist[i]*y*5)--((i + 1)*x,0)--cycle);
label(string(i),((i + 0.5)*x,0),S,fontsize(6));
label(string(hist[i]),((i + 0.5)*x,hist[i]*y*5),N,fontsize(8));
}
[/asy]](http://latex.artofproblemsolving.com/2/8/f/28f966299e2e508fd867e79ead08ba8b4e7b4df4.png)
![[asy]
unitsize(1cm);
real x, y;
real[] hist = {30, 28, 28, 19, 25, 19, 27, 16, 7, 23, 4, 6, 8, 1, 0};
x = 0.75;
y = 0.15;
draw((x,0)--(15*x,0));
for(int i = 0; i < 15; ++i) {
draw((i*x,0)--(i*x,hist[i]*y)--((i + 1)*x,hist[i]*y)--((i + 1)*x,0)--cycle);
label(string(i + 1),((i + 0.5)*x,0),S,fontsize(6));
label(string(hist[i]),((i + 0.5)*x,hist[i]*y),N,fontsize(8));
}
[/asy]](http://latex.artofproblemsolving.com/6/7/1/671e37eda8d80c5544dd189c426ea5c9aa1749cb.png)
This post has been edited 23 times. Last edited by Emathmaster, Jan 23, 2021, 5:56 PM
,
