Time for our new winter challenge! This time our challenge has also two Computer Science related questions and a separate section with five High School math problems. Enjoy!
Rules:
a) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be...
Merry Christmas to all who celebrate it today!
Rules:
a) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions will be posted around 15th of the following month.
b) It is fine to use nontrivial results without proof as long...
Summer is coming and brings a new intermediate math challenge! Enjoy! If you find the problems difficult to solve don't be disappointed! Just check our other basic level math challenge thread!
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no...
Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread!
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions will...
It's time for a basic math challenge! For more advanced problems you can check our other intermediate level math challenge thread!
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results...
We, a small group of currently four members, want to try a new version of the math-challenges-threads once a month. It turned out to be not as easy as we thought, to find good problems. So what we've gathered are ten questions on "B" level and ten on "I" level for May, and plan to do the same...
Submitted by: @QuantumQuest
Challenge Level: High School
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common...
Submitted and judged by: @QuantumQuest
Solution credit awarded to: @ddddd28
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as...
I have a reversible chemical reaction described by the balanced equation: ##aA+bB=cC+dD##. I devise a reversible process to take a closed system containing these species (and its surroundings) from thermodynamic equilibrium state 1 to thermodynamic equilibrium state 2:
State 1: a moles of...
Submitted and judged by: @QuantumQuest
Solution credit: @MAGNIBORO
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is...
Submitted and Judged by @QuantumQuest
Solution credited to: @TSny
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is...
Submitted and judged by: @Erland
Solution Credit: @SSequence for 2a, 2B, C, D
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long...
Submitted by @Erland
Solution Credit: @mfb
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all...
Hey all, I have a unit test tomorrow on Gravitational and Electric Fields. If you have any good practice questions for Grade 12 University level please leave them below! :)
In my class we've learned gravitational force, gravitational field strength and orbits (omit geosynchronous) as well as...
Time for the october challenge! This time a lot of people sent me suggestions for challenges. I wish to thank them a lot! If you think of a good challenge that could be included here, don't hesitate to send me!
Ranking [and previous challenges] here...
September, schools restart, summer ends, but a new challenge is here:
Ranking here: https://www.physicsforums.com/threads/micromass-big-challenge-ranking.879070/
RULES:
1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
2) It...
August is already well underway, so time for some nice challenges! This thread contains both challenges for high schoolers and college freshmen, and for more advanced people. Also some previously unsolved challenges are omitted.
Ranking here...
Homework Statement
You have been employed but(sic) the Mathematics Football League (MFL) to design a football. Using the volume of revolution technique, your football design must have a capacity of 5L ± 100mL. You must present a statement considering the brief below. Just a quick side note, I...
Here is a thread of challenges made especially for high school students and first year university students. All the following problems can be solved with algebra, trigonometry, analytic geometry, precalculus and single-variable calculus. That does not mean that the question are all easy.
For...
Summer, July, hot weather: every reason is good enough for some new challenge questions.
NEW: ranking can be found here: https://www.physicsforums.com/threads/micromass-big-challenge-ranking.879070/
For high school and first year university students, there is a special challenge thread for you...
List of challenges:
Integral Challenge: https://www.physicsforums.com/threads/micromass-big-integral-challenge.867904/
Counterexample Challenge: https://www.physicsforums.com/threads/micromass-big-counterexample-challenge.869194/
Counterexample Challenge 2...
In this thread, I present a few challenging problems from all kinds of mathematical disciplines.
RULES:
In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored.
It is fine to use nontrivial results without proof as long as you cite...
We had integrals, so we have to have series as well. Here are 10 easy to difficult series and infinite products. Up to you to find out the exact sum.
Rules:
The answer must be a finite expression. The only expressions allowed are integers written in base 10, the elementary arithmetic...
Probability theory is very nice. It contains many questions which are very easy to state, but not so easily solved. Let's see if you can solve these questions.
For an answer to count, not only the answer must be given but also a detailed explanation.
Any use of outside sources is allowed, but...
And we continue our parade of counterexamples! Most of them are again in the field of real analysis, but I put some other stuff in there as well.
This time the format is a bit different. We present 10 statements that are all of the nature ##P## if and only if ##Q##. As it turns out, only one of...
Well, the last thread of counterexamples was pretty fun. So why not do it again! Again, I present you a list with 10 mathematical statements. The only rub now is that only ##9## are false, thus one of the statements is true. Provide a counterexample to the false statements and a proof for the...
I adore counterexamples. They're one of the most beautiful things about math: a clevery found ugly counterexample to a plausible claim. Below I have listed 10 statements about basic analysis which are all false. Your job is to find the correct counterexample. Some are easy, some are not so easy...
Integrals are pretty interesting, and there are a lot of different methods to solve them. In this thread, I will give as a challenge 10 integrals. Here are the rules:
For a solution to count, the answer must not only be correct, but a detailed solution must also be given.
A correct answer...
Homework Statement
A solid cube of side ##l = r*pi/2## and of uniform density is placed on the highest point of a cylinder of radius ##r## as shown in the attached figure. If the cylinder is sufficiently rough that no sliding occurs, calculate the full range of the angle through which the block...
Do you have very hard problems about work? I referred to my algebra book and googled in vain. Not talking about the product of the force magnitude and the displacement magnitude. This is what I’m talking about – Jennifer takes 4 hours to do a job. John takes 6 hours to do the same job. Working...