@MichaelHale It's one of the less interesting questions, but I think that one of my favourite WL "killer apps" is the tracking of units like in question 3.

Yeah, that was one of the reasons I wanted to do the test, was use some features that I don't normally use. The Ctrl+= input worked smoothly for all of the unit combinations. But that was my first time using the net access since the 12.1.1 upgrade I guess, so I had to sign in again otherwise it just gave a cryptic no internet access error, despite network test succeeding.

I wish we had more transparency into why like #13 needed so much guidance.

@MichaelHale 12.1.1 was able to solve #13 directly for me, although it did take a few minutes.

Alright. I'll give it an hour. It's been going for 15 min or so I think.

Solve[(((n^(1/c)) n)^(1/b) n)^(1/a) == n^(25/36) && a > 1 && b > 1 &&
  c > 1 && {a, b, c} \[Element] Integers, b]

Oops, forgot constraint on n, I'll restart it.

I did:

takes about 5 minutes for me

Solve[(((n^(1/c)) n)^(1/b) n)^(1/a) == n^(25/36) && a > 1 && b > 1 &&
  c > 1 && {a, b, c} \[Element] Integers && n > 1, b, Reals]

But I figured that was redundant given each variable has an inequality associated with it.

interesting!

And then if I write it with radicals I immediately get a message saying it can't be solved with available methods

Solve[Surd[n Surd[n Surd[n, c], b], a] == Surd[n^25, 36] && a > 1 &&
  b > 1 && c > 1 && {a, b, c} \[Element] Integers && n > 1, b, Reals]

I also get ~6s using Reals:

which only makes your point, the system seems to need quite a bit of guidance

I'm going to submit that as an issue

Cool. I was considering the same. I mean, it seems like if it can do it quickly with those little bits of redundant guidance that it should be able to do it quickly as first entered.

#22 had a smooth progression of attempts. First try Sum, then NSum, then just Total@Table

So I at least had a progression of more manual fallbacks to try that is relevant across a variety of problems.

19, 21, and 25 I had no idea on though

Interesting to compare these three

w/y /. Solve[{w/x == 4/3, y/z == 3/2, z/x == 1/6}]

Solve[{w/x == 4/3, y/z == 3/2, z/x == 1/6, w/y == answer}]

Solve[{w/x == 4/3, y/z == 3/2, z/x == 1/6, w/y == answer}, answer]

Last one says no solutions for me. Technically one argument version of Solve isn't documented either. Sent feedback.

would be interesting to see if someone has done a Maple comparison

I've definitely seen some comparison discussions about Maple with regards to solving integrals. I think Wolfram put in a pretty successful effort to catch up. Haven't seen a Maple run for these problems.

I think you are confusing the sum having 137 terms with the power of the 137th term being 137.

@MichaelHale aha, thank you, reading comprehension problem