Below are six small code-golf brainteasers that I originally wrote for PPCG SE but are now off-topic for that site. The solutions mostly involve tricks that I've used or seen in the past.

Problem 1
Output the following list: {10,15,21,28}; that is, the 4th through 7th triangular numbers.

//15 bytes:

Problem 2
Given an integer in Ans representing an integer between 1 and 10000000, output the number of factors of 2 that divide it.

//31 bytes
While X/2=int(X/2

Problem 3
Given a list with 2 or more elements in Ans, output 0 if all of its elements are the same, and a nonzero value if any of its elements are different.

//6 bytes

Problem 4
Given a list in Ans of at least 4 integers from 1 to 6, determine if there is a sublist of four elements that form either two pairs or four of a kind: for example, 5,5,6,6, 1,4,4,1, and 3,3,3,3 are all sublists. Output a nonzero value iff there is at least one.

//??? bytes

Problem 5
Given a list in Ans of positive integers, calculate their harmonic mean.

//8 bytes

Problem 6
Given a list of integers in Ans, find the sum of the elements greater than its minimum.

//10 bytes

Please hide any spoilers if you solve the problems.

EDIT: Fixed a couple of reference solutions.
Problem 1, 11 bytes: cumSum({10,5,6,7

Problem 2, 15 bytes: sum(not(fPart(Ans/2^cumSum(binomcdf(23,0 Explanation: This counts how many powers of 2 are factors of Ans, which is the same as the amount of factors of 2. It works because if X is not a factor of Ans, X*2 isn't either, so that's why I can just do sum(not(fPart(

Problem 3, 5 bytes: max(Ans≠max(Ans

Problem 4, 21 bytes: 3<sum(1<seq(sum(Ans=Ans(X)),X,1,dim(Ans Explanation: For each element it counts how many elements have the same value. If that's more than 1, there's a pair with the else element(s). However, since the other element has it as well, and there are 2 pairs, the amount of (sum of amount of elements with value of elemtn X) should be at least 4. This applies to 4 same elements as well, all 4 have 3 other elements.

Problem 5, 7 bytes: dim(Ans)/sum(Ans^^-1

Problem 6, 7 bytes: sum(Ansnot(Ans=min(Ans

Your answer to problem 2 is wrong, because While X=int(X/2 doesn't loop at all.

Your answer to problem 3 is wrong, it returns 1 when all elements are the same.
Problem 2, 16 bytes: :sum(not(fPart(Ans/seq(2^X,1,24

I had a suspicion it could be one-lined...

Remark: P_T and I seemed to have found this one at about the same time!
Remark 2: Looks like you can drop a byte on this solution. See P_T's answer for that one.

Problem 3, 5 bytes: max(abs(ΔList(Ans

Problem 5, 5 bytes: mean(Ans⁻)⁻
I'll just post an 8-byter for Problem 1 based on a wonderful trick I espied you using recently: timeCnv(919288

Then there's the overly-expensive now-passable solution 2412→rand:int(37rand(4, which I had Mathematica spit out for me, to boot.

No ingenuity here today. Just cheats.

PT_: Regarding the core of your Problem 2 solution, the argument should generally be one less than the intended dimension/maximum. While its counterpart goes from 0N, it itself will take on 1N+1.
Problem 4, 18 bytes: 2<=sum(iPart(.5seq(sum(Ans=X),X,1,6
Explanation: For each integer X from 1 to 6, count the number of elements equal to X. Floor-divide these counts by 2, so integers appearing 0 or 1 times produce 0, integers appearing 2 or 3 times produce 1, integers appearing 4 or 5 times produce 2, etc. Sum these divided counts and check if greater than or equal to 2.
Oops, I intended problem 4 to read
"Given a list in Ans of at least 4 integers from 1 to 6, determine if there are four *consecutive* elements that form either two pairs or four of a kind: for example, 5,5,6,6, 1,4,4,1, and 1,2,3,3,3,3 all qualify but 2,3,4,3,2 does not. Output a nonzero value if so and zero if not." Let's call the original version 4A and this 4B.

EDIT: Weregoose's solution for 1 was the intended solution. Runer's for 4A looks optimal. No one has optimal solutions for 2, 3, 4B, or 5 yet.
I think this works for 2:
Problem 2, 13 bytes: sum(not(fPart(Ans/2^randIntNoRep(1,23 Explanation: same as PT_'s solution, but it doesn't matter if they are in order or not

and I think this works for problem 3:
Problem 3, 4 bytes: min(ΔList(Ans

I haven't tested either one though.
Dunno how I happened upon this thread, but here is what I can offer off the top of my head:

Problem 2: 5 bytes: gcf(2,Ans 11 bytes: int(.5gcd(Ans,2^23

Problem 3: 3 bytes: variance(Ans

When I find a solution to Problem 4B, I'll post.

I have provided no descriptions.


Correction to #2: 12 bytes: log(gcd(Ans,2^23),2

Problem 4B: 10 bytes: max(not(deltaList(abs(deltaList(deltaList(Ans
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