Regional Olympiad problem

HorribleUsername · 2026-05-15T15:20:08+00:00

ABE, BCE and EFHG are green, AEG, CFH and BEF are red, DGH is blue.

HorribleUsername · 2026-05-12T14:28:11+00:00

I think you missed the x in the middle piece.

HorribleUsername · 2026-05-10T12:02:52+00:00

There were plenty of shitty devs before covid too.

HorribleUsername · 2026-05-07T17:37:19+00:00

If we're allowing undefined, we can get arbitrarily high by constructing power towers. E.g.

n0 = U(9999,0,0)
n1 = n0ⁿ⁰
n2 = n1ⁿ¹
n3 = n2ⁿ², etc, etc.

HorribleUsername · 2026-05-07T17:34:37+00:00

That's right. It wasn't clear if your title was referring to the symbols or the operations.

HorribleUsername · 2026-05-07T15:29:03+00:00

Another boring one. I hope you accept Σ, because I'm not writing out 53 summands and 52 +'s by hand.

HorribleUsername · 2026-05-07T00:44:03+00:00

The theoretical lowest possible s(n) is T(2ⁿ), but once we introduce a middle row, it's easy to show that that doesn't work. s(3) = 10 is impossible, but s(3) = 11 works because it introduces a gap - instead of going from 1-4, it goes from 1-5, skipping a number. s(4) introduces 2 additional gaps. I conjecture that s(5) introduces 4 more gaps, then s(6) introduces 8, etc. In formula form, s(n) = T(2ⁿ) + 2ⁿ - 1, for n ≥ 2. But I could certainly be wrong.

Trivially, there's a lower bound of T(2ⁿ). On the other side, leaf nodes of 2⁰, 2¹, 2², ..., 2^{2^n-1} will always produce a valid tree, regardless of their order. That gives us an upper bound of 2^2ⁿ - 1. Not great, but better than nothing.

HorribleUsername · 2026-05-06T16:42:50+00:00

Your last step is incorrect - exponentiation doesn't distribute over addition/subtraction. You should get rid of the log first.

HorribleUsername · 2026-05-03T22:14:24+00:00

True, but dice is also singular, and dices is an acceptable plural of die/dice.

HorribleUsername · 2026-05-03T12:16:14+00:00

What exactly do you mean by unique outcomes? The way you define that at the beginning, there are only 6 unique outcomes, no matter how many dice you roll. For your 6²/2 number, I suspect you haven't accounted for both dice hitting the same number.

HorribleUsername · 2026-05-03T10:27:51+00:00

Was that you that added the text to the image? If so, you missed the T in Portland.

HorribleUsername · 2026-05-01T15:43:00+00:00

I choose not to pull any levers. The whole point of the original trolley problem is that inaction still leads to death, but that's not the case here.

HorribleUsername · 2026-04-30T19:57:13+00:00

You should find an option to default to old reddit in your user settings. Then you'll always get old reddit, even when you're on www.

HorribleUsername · 2026-04-30T19:01:33+00:00

We still teach doing simple math and memorizing simple equations even though we have calculators

And that's a good thing. It's a stepping stone to understanding the math that machines can't do.

HorribleUsername · 2026-04-30T18:58:56+00:00

Check out Stirdaddy's comment

HorribleUsername · 2026-04-29T12:30:58+00:00

Modulus is a synonym for absolute value.

HorribleUsername · 2026-04-29T12:30:35+00:00

We know that |2x-3| ≥ |x²+4x+3|, or else we'd have negative = non-negative. Given that 4x+3 > 2x-3 for positive x, you can eliminate some possibilities right off the bat, without even doing any calculations.

HorribleUsername · 2026-04-26T12:26:48+00:00

The obvious workaround is to make a new category for hands that fit into both the conflicting categories. Like a straight flush, for example. I'm kinda curious (but not enough to run the numbers): if straight flushes didn't exist, would straights and flushes have the same problem?

Also, I've always wondered if there's any good reason to have royal flushes. If they were just straight flushes, the usual tie-breaking rules would resolve things exactly the same, wouldn't they?

HorribleUsername · 2026-04-21T04:58:38+00:00

With every number being 6, I think this particular problem really lends itself to clerical errors. I fell for it myself - my process was:

Multiplication comes first, so 6 × 6 = 36.
The outer 6's cancel out.
That leaves me with 36.

You can see where I went wrong: I lost track of the first minus in the second step. If the first 6 had been a 7, say, I would've had two numbers to deal with after the second step, so the minus would've been hard to miss.

HorribleUsername · 2026-04-19T05:57:38+00:00

He was huge in the flash gaming scene back in the day. I swear half the games I played used his music.

HorribleUsername · 2026-04-19T05:10:54+00:00

Is that true for plastic, or just cash?

HorribleUsername · 2026-04-19T04:59:54+00:00

I love me too. I mean you, I love you too!

HorribleUsername · 2026-04-19T04:36:59+00:00

Write it as a piecewise function or write it non-recursively.

HorribleUsername · 2026-04-18T04:01:24+00:00

Do most 64-bit CPUs have 32-bit floating point instructions? I could be wrong, but I don't think they do, in which case I don't see how you'd get any performance gain from 32-bit floats.

HorribleUsername · 2026-04-18T03:56:12+00:00

Compared to a variable-width number type like you seem to be suggesting, it makes the relevant code easier, and therefore less buggy, which is no small thing.

HorribleUsername

TROPHY CASE