User talk:Ddk001

$[asy]draw((0,0)----(0,6));draw((0,-3)----(-3,3));draw((3,0)----(-3,6));draw((6,-6)----(-6,3));draw((6,0)----(-6,0));[/asy]$

User counts

If this is your first time seeing this section, please edit it by adding the number by 1.

$\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{2}}}}}}}}}}}}}}}}$

Again, as said, this looks like a number on a pyramid.

Problems

Solutions

If you have solved the problems in my user page, put your solution here. We might have a discussion about the solution, like we will on a forum.

New Problems

If you have a problem to contribute, please put it here. I might add it to my user page. If I have a set of $15$ good problems, we can consider starting a mock AIME or we can perhaps get the problems into future AIME.

Note: I am talking mostly of AIME because my problems are mostly AIME based. If you have AMC or olympiad problems to contribute, you are welcomed to put it here.

Weird expressions

Here is the contest where you try to come up with the with the weirdest expression. Here a record to break:

$\frac{(\frac{\sqrt{3223}+\sqrt[23]{9879e}}{293847}+398\pi)^{9812347^{23478^{3^3}}}}{\sqrt[123]{\frac{\sqrt{\sqrt[23e]{3948 \pi}+(\sqrt{\frac{(19203e+\sqrt{\frac{\frac{(\frac{\sqrt[3e]{\frac{\frac{\frac{3}{4}}{\frac{4e}{3}}}{\pi}}}{\sqrt{10101010}}+121\pi)^{23}}{1902\pi e+10} \cdot (\frac{\sqrt[20202023e]{\frac{\frac{\frac{3243234}{4234}}{\frac{1023}{323}}}{23\pi}}}{\sqrt{1230}}+23189\sqrt{2}+29384)^{12}}{192019\sqrt{\frac{232}{2093}}+29384\pi}})^{10}}{1029\sqrt{23}+92483\pi+121212}}+1304987\pi)^{\sin{12394} e}}}{(\sin{(\sqrt{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}+\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{23}}}}})}+\cos{(\sqrt{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}+\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{23}}}}})})^{12e}}+\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{18743691}}}}}}}}}$ ~Ddk001

Be sure to include the owner of the expression. If you thought of another one, do not delete the existing ones. Simply add the new one.

Talk

Hi! You can say anything here. Please include who is talking. ~Ddk001

hi -l.m.

Hi!~Ddk001

HI DDK, SANSKAR'S OG PROBLEMS do check this out also please tell me when you are free like at what time so that we can exchange some problems and discuss them. BY THE WAY PLEASE MENTION THE TIME ZONE AS WELL BECAUSE I AM IN INDIA~ SANSGANKRSNGUPTA

I'm free sometimes in the evening (7:00-9:00 pm, Central time US). I would love to exchange problems and solutions :D Most of the problems are on my user page.~Ddk001 Also @SANSGANKRSNGUPTA, I created the 2023 IOQM Problems and added content. I can't get the latex of problem 19 to work, though.~Ddk001

Hi Ddk, thanks for doing so. https://www.mtai.org.in/wp-content/uploads/2023/09/IOQM_Sep_2023_Question-paper-with-answer-key.pdf

YOU CAN REFER TO THIS FOR CONTRIBUTING AND ADDING THE REMAINING PROBLEMS IN IOQM 2023 PAGE, https://www.mtai.org.in/wp-content/uploads/2023/09/IOQM_Sep_2023_Question-paper-with-answer-key.pdf

ALSO, DDK YOUR SOLUTION TO THE FIRST PROBLEM OF SANSKAR'S OG PROBLEMS HAS SOME MISTAKES, AND FOR P1 THERE DO EXIST SOME A AND B SO DO TRY AGAIN!

AND THANK YOU VERY MUCH ONCE AGAIN. DON'T DELETE YOUR SOLUTION EVEN THOUGH IT HAS A MISTAKE JUST LET IT BE THERE AND A NEW SOLUTION, ALSO THESE DAYS I AM TOO BUSY DUE TO SOME STUFF SO PROBABLY I WON'T BE ABLE TO CONVERSATE IN A TIMELY MANNER TILL 10 MARCH, WILL ALSO SOLVE PROBLEMS ON YOUR USER PAGE WHEN I GET TIME. THANKS AGAIN~ SANSGANKRSNGUPTA

Things I think is interesting

The purpose of aops is to "Train today's mind for tomorrow's problems". I will now prove that this is impossible.

Suppose, for the sake of contradiction, that "Train today's mind for tomorrow's problems" is possible. Since we have problems today (Day 1), the base case is taken care of. Now, assume that we have problems on Day $k$ . Then, since we are training today's mind for tomorrow's problems, there will be problems on the next day, Day $k+1$ . Hence, by induction, there will be problems every day. This would imply there is infinitely many problems, a contradiction. Hence, the assumption, "Train today's mind for tomorrows problems", is incorrect.

Tell me if you see any flaws in this proof.

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