R, 9 bytes F:volcano Try it online! The sequence operator : coerces its arguments to integers. F is the boolean FALSE, which gets coerced to 0. volcano is one of the many built-in datasets (it gives ...

R, 23 bytes x=rnorm(3) x/(x%*%x)^.5 Try it online! Generates 3 realizations of the $\mathcal N(0,1)$ distribution and normalizes the resulting vector. Plot of 1000 realizations:

Grass, 17 bytes wWWwwwVVwWWwWWWww Try it online! -2 bytes thanks to jimmy23013. Outputs www. Grass ignores all characters apart from w, W and v. The two Vs are thus ignored; they are there to ...

Proof of impossibility The only anti-distributive operator when $S=\mathbb Z$ is such that $\forall a, \forall b, a*b=0$. Indeed, suppose that $*$ is anti-distributive. Then $*$ has the ...

R, 63 59 bytes s=scan()%%c(2,3,5,7);i=which(s<c(0,2,3,5));any(s[i]-s[i-1]) Try it online! -4 bytes thanks to Giuseppe (The explanation contains a spoiler as to how to solve the problem without ...

R, 34 bytes # d= cat d(9^ (1:7) ,sep=" ")##### Try it online! Outputs $9^1$ to $9^7$: 9 81 729 6561 59049 531441 4782969

Unreadable, 789 777 bytes -12 bytes by using variable X34 rather than X6. '""""""'""'"""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'""'"""'"""""...

R, 66 35 bytes -29 bytes thanks to digEmAll. -2 bytes thanks to Giuseppe. +0->A x=!0:F F=F+1 sample(F*x+!x,1) Try it online! Check the distribution for N=4. The key is the rightwards ...

Random 50-90 If the average is $m$, the optimal play is $50+0.4m$. If we assume the average is uniformly distributed over $[0, 100]$, the optimal play is uniformly distributed over $[50, 90]$. ...

R, 43 41 bytes cat(T+F:T,"miss a few",3*33+F:T,sep=", ") Try it online! T and F are equal to TRUE and FALSE. They get coerced to integers 1 and 0 by the operators + and :.

R, 59 bytes function(x)nlm(function(y)max(Mod(x-y%*%c(1,1i))),0:1)[1:2] Try it online! Takes input as a vector of complex coordinates. Mod is the distance (modulus) in the complex plane and nlm is ...

R, 26 25 24 bytes -1 byte thanks to Dominic van Essen repeat cat(rpois(9,9)+1) Try it online! Outputs a random infinite sequence of integers, drawn from the $Poisson(9)$ distribution (+1 to avoid ...

Shakespeare Programming Language, 221 bytes ,.Ajax,.Puck,. Act I:.Scene I:.[Enter Ajax and Puck] Ajax:You cat. Scene V:. Puck:You is the sum ofYou a cat. Ajax:Open heart.Is I nicer you?If notYou is ...

R, 53 38 bytes function(x)c(x%/%5,2*x%%1,(x<20)*x%%5) Try it online! Output is in the order (5mg, 2.5mg, 1mg). For the 2.5mg pills: if the dose is an integer, we need 0 such pills. Indeed, 1 ...

Shakespeare Programming Language, 329 bytes ,.Ajax,.Page,.Act I:.Scene I:.[Enter Ajax and Page] Ajax:Listen tothy. Page:You cat. Scene V:. Page:You is the sum ofYou a cat. Is the remainder of the ...

R, score=67.47 47.92 30 bytes, MSE = 0.54587 -1 byte (and -1.47 in score) thanks to Dominic van Essen. pnorm(scan(),31,41,F)*scan()-2 Try it online! The input format is: age as an integer, then a ...

R, 61 bytes cat(paste0(c(" 1 ",""," ","9 "," ",""," "),sample(2:8))) Try it online! Prints alternately the proper whitespace/newline (with 1 and 9 included) and elements of a random ...

R, 82 75 67 62 bytes -4 bytes thanks to Giuseppe. !-1->i c(tail(s<-el(strsplit(scan(,""),"")),1/i),head(s,-i))#! Try it online! ry it online!T !Try it online Uses rightwards assignment -&...

R, 39 bytes n=scan();n*rgeom(1,1-1/n)+sample(n-1,1) Try it online! Explanation: this solution avoids recursion/while loops by directly calculating the distribution of the number of explosions that ...

Shakespeare Programming Language, 258 252 bytes -6 bytes thanks to the default. ,.Ajax,.Puck,.Act I:.Scene I:.[Exeunt][Enter Ajax and Puck] Ajax:Open mind. Puck:Is I nicer zero?If soYou is the sum ofI ...

R, 23 bytes function(m)!any(m+t(m)) Try it online! Checks whether there are any non-zero elements in $M+M^T$.

180 white squares My strategy was simply to find a smaller rectangle with no black squares, such that it can be filled in uniquely. All 2×k rectangles have multiple solutions. For 3×k rectangles, ...

R, 114 107 bytes -5 bytes thanks to Giuseppe. Outgolfed by digEmAll. function(l){for(j in seq(l))l[j]=rep(l[j]%/%(e=10^(b=nchar(l[j]):1-1))%%10,j+1)[j+0:b]%*%e sum(sort(l)==l)} Try it online! 0-...

R, 43 39 bytes -4 bytes thanks to Giuseppe. for(i in 1:scan())T=T%/%i^(2*(i<T)-1);T Try it online! Outputs the $n$th term, 1-indexed. Initializing the sequence with $a(0)=1$ also works, as ...

R, 60 bytes, cracked by Paul function(x) chartr("zyxwvu", "RRRRRR", tolower(x + x)) Try it online! As in my previous challenge, the flag to output is the string "R&...

R, 68 bytes function(M,m,n,A=M){while(any(A%*%M%%m!=diag(n)))A[]=rpois(n^2,9) A} Try it online! Strikingly slow. Will most likely time out for all test cases on TIO, but is guaranteed to give an ...

R, 40 bytes function(x)min(x)+max(x)+mean(sign(x))<0 Try it online! If min(x)+max(x) is non-zero, its sign corresponds to the note farthest from the centre and gives the direction of the beam. ...

R, 70 69 67 bytes x=scan();?=mean;while(x-?x)x=c((?x^2)^.5,?x,2^?log2(x),1/?1/x);?x Try it online! -1 byte with better conditioning.-2 bytes by switching to base 2. Like some other answers, this ...