0
3
Determine all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$(x-2)f(y)+f\big(y+2f(x)\big)=f\big(x+yf(x)\big)$$ for all $x,y\in\mathbb{R}$.
Source will be given after the problem is solved, or the solution to the problem can be easily found.
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Find all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying the following functional equation: $$f(\lfloor x\rfloor y)=f(x)\lfloor f(y)\rfloor\quad\quad\text{for all }x,y\in\mathbb{R},$$ where $\lfloor\cdot\rfloor$ is the floor function (largest integer less than or equal to its argument).
(Pendin...
Yep, this is my 100th puzzle here in PSE~
I'm really having a wonderful time here, thank you so much guys! ><
I planned to write a harder and bigger one, but it turned out I was too lazy to do that..
So anyway, this is Minesweeper (Mine Clones)!
Rules:
Put exactly 100 mines in the e...
Start with a bag containing one red marble and one white marble.
Reach into the bag and pull out a marble at random.
Put it back and do it again.
If, on both times, you grabbed the red marble, stop.
Otherwise add two white marbles to the bag and repeat these steps.
What is the probability ...
0
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This is in regards to the solution in Slitherlink - It's all in the 2s
I know it may seem dumb, but I don't understand the logic behind the second 2 chain in the solution. To help provide clarity in my question, imagine that each dot corresponds to a Letter-Number coordinate like
7
6
5
4...
Stuck with this for long time now, I have tried all the techniques yhat I know
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Here on Puzzling, we're a little different from other sites. Like, we know the answers before we post the question (usually), and we want other people to come to the same conclusion. And sometimes, we work on puzzles with other people. Take my Clues series. There is a list of Clues, and the puzz...
