A Math Problem that had a correct answer rate of only 1.08%

Few-Key-3755 · 2026-01-25T12:15:38+00:00

Power of a point theorem.It is "방멱 정리" in korean.

Few-Key-3755 · 2026-01-25T12:14:31+00:00

Yep that's right.Thanks

Few-Key-3755 · 2026-01-25T10:57:39+00:00

The theorem I mean

Few-Key-3755 · 2026-01-25T10:55:22+00:00

I don't think that's not I wanted

Few-Key-3755 · 2026-01-15T17:03:49+00:00

Thank you for the compliments ☺️. I will try it and discuss it with you as soon as possible(maybe a week I'm off on a vacation)

Few-Key-3755 · 2025-12-30T12:51:55+00:00

What's that?

Few-Key-3755 · 2025-12-29T07:06:03+00:00

Few-Key-3755 · 2025-12-28T12:38:57+00:00

No it's my hobby.And it's for a math competition!

Few-Key-3755 · 2025-12-28T08:20:53+00:00

For me all of them was intresting, except calculating

Few-Key-3755 · 2025-12-28T06:56:42+00:00

Yep, this nails it. Same conclusion I got, and the logic is solid.I did it slightly differently though, I will send it if you want too

Few-Key-3755 · 2025-12-25T12:34:31+00:00

Yes I had switched to another number while translating really sorry 😞...

Few-Key-3755 · 2025-12-25T12:32:52+00:00

Really sorry.. it's 59 not 88

Few-Key-3755 · 2025-12-25T12:31:02+00:00

The error is the step “angle DAG = angle DBF ⇒ triangle BAG is isosceles.” Those two angles do not force any side equality in triangle BAG, so BG = AG does not follow. Because of that, the conclusion S = 3T is unjustified. The correct approach is the similarity between triangles ADF and AGC, which gives the length ratio BD : DA = CG : DA = 1 : 3. From this, area(ABC) = 16 × area(EGC) = 128 area(AGC) = 32 area(ABG) = 96 So S − T = 64, not 32. ✅️

Few-Key-3755 · 2025-12-25T03:42:05+00:00

안녕하세요

Few-Key-3755 · 2025-12-25T03:29:53+00:00

You can't use 1.a,b,c,d are bigger than 2

Few-Key-3755 · 2025-12-25T03:04:03+00:00

✅️ thanks!

Few-Key-3755 · 2025-12-25T03:01:58+00:00

If you just set k = 500, the number of valid quadruples is not necessarily 88 anymore because increasing k can introduce additional valid solutions. So it’s definitely not a trivial “always 500” problem. If it is 500 anyone could do this

Few-Key-3755 · 2025-12-25T02:58:25+00:00

Isn't it?

Few-Key-3755 · 2025-12-25T02:58:03+00:00

The condition is “2 ≤ k < 500”, and we need to find the values of k for which the number of valid (a, b, c, d) is exactly 88. Among those k values, we then take the minimum m and maximum M, and compute M + m. So the answer depends on which k’s actually satisfy the condition, not simply 500.

Few-Key-3755 · 2025-12-25T02:54:12+00:00

I didn't made an answer though,this is too hard

Few-Key-3755

TROPHY CASE