This is a variant some of the existing questions on this exchange, but I can't see this exact problem. Basic example Some prisoners are going to be lined up, all facing forward. A hat, either black or white, will be placed on their head. The prisoners at the back of the line can see all of the h...

So for example: if N = 3 I roll and get -> 1,2,3 I re-roll the 2 and 3 -> 1,4,4 I re-roll the 1 -> 2,4,4 I re-roll the 2 -> 4,4,4 In this case, it took 4 rolls for N=3 but what is the average number of rolls for N?

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f(x)f\big(f(x)+y\big)=f\big(x^2\big)+f(xy)$$ for all $x,y\in\mathbb R$ Problem by me

For context, here is my previous puzzle in this format. Me, I cause pain. My first anagram is naturally beautiful. My second anagram is synonymous with rocks. My third anagram is fancy food. My homophone is what two brothers wanted humanity to do. My homophone’s anagram can direct and achieve mo...

May be this problem is already answered. I am not aware. What is the next number in the following series? Importantly, after that number, are there any more numbers? is there a math related reason for that? 1, 512, 4913, 5832, 17576, ?