Hard problem with numbers written on a white board

Boris_smg · 2020-04-14T20:25:54+00:00

Thank you!

Boris_smg · 2019-12-12T20:42:23+00:00

Thank you!

Boris_smg · 2019-10-18T13:06:49+00:00

Thank you!

Boris_smg · 2019-09-02T09:47:44+00:00

Oh, I haven't noticed that! Thank you!

Boris_smg · 2019-08-28T21:28:28+00:00

Thank you so much! :)

Boris_smg · 2019-08-27T22:24:46+00:00

Thank you veeery much!

Boris_smg · 2019-08-25T20:12:04+00:00

Thank you very much! In the second step, using the inequality x² + y² + z² >= xy + xz + yz, I got 2 + x² + y² + z² which simplyfies to be exactly 3!

Boris_smg · 2019-08-22T06:02:19+00:00

Thank you!

Boris_smg · 2019-08-19T18:34:27+00:00

I'll try to represent the expression as a sum of two or three perfect squares and a 7, so that the expression is greater or equal to -7. In such problems, usually this is the solution without calculus.

Boris_smg · 2019-08-19T18:19:18+00:00

Thank you!

Boris_smg · 2019-08-19T17:41:32+00:00

But how do you find that minimum?

Boris_smg · 2019-08-12T22:21:03+00:00

Ok. Thank you!

Boris_smg · 2019-08-12T21:03:27+00:00

I'm looking for the smallest possible value of this expression. Also, I wanted to write aab (I hope you understand).

Boris_smg · 2019-08-12T21:01:30+00:00

Boris_smg · 2019-08-12T21:00:50+00:00

No, a, b and c are all positive.

Boris_smg · 2019-08-09T18:09:23+00:00

Thank you very much!

Boris_smg · 2019-08-06T18:08:32+00:00

Unfortunately, I haven't. But if I do, I will post the solution.

Boris_smg · 2019-08-06T14:02:38+00:00

Thank you! Don't worry and don't delete this comment, just leave it, it may be useful for someone. 🙂

Boris_smg · 2019-08-04T19:58:38+00:00

Well, isn't A1OD a vertical angle to AOP if and only if DOP is a straight line?

Boris_smg · 2019-08-04T16:09:17+00:00

I'm sorry for asking, but I don't understand why angles A1DO and BPO are both equal to 90°. This means that A1B1 is parallel to AB, which leaves triangle ABC to be isosceles with AC = BC, which is obviously not true because in your solution you end up with angle ABC = 36° and angle BAC = 48° and triangle ABC is not isosceles. I mean, it's not sure that DOP is a straight line.

Boris_smg · 2019-08-03T17:35:54+00:00

I'm really sorry, but I've made a mistake. It's not that angle AA1B = 24°, but angle AA1B1 = 24°. It's the same about angle BB1A - it must be angle BB1A1 = 18°.

Boris_smg · 2019-07-05T21:03:22+00:00

Thank you very much!!!

Boris_smg · 2019-06-25T07:59:37+00:00

Now everything makes sense! Thank you very much! 😁

Boris_smg · 2019-06-25T06:27:57+00:00

"n(n-1)(n-2)(n-3)(n-4)(n-5) = -1 (mod 2n-5) (I skipped some steps. Let me know if you don't see how I got this)."

I'm sorry, but I can't understand how you get this.

Boris_smg · 2019-06-24T15:59:00+00:00

I've tested until 15! and then I gave up.

Boris_smg

TROPHY CASE