Anything is possible, unless it's not

Saturday, November 13, 2010

Can you solve these problems?

(Problem 1.) Given real constants a, b, c, ... , z
that satisfies a5 = b; b5 = c; c5 = d; ... ; y5 = z
If a = 2010, find the value of (x-a)(x-b)(x-c)...(x-z).

(Problem 2.) Find the value of cos(1) cos(2) cos(3) ... cos(2010).
Note: cosines are expressed in degrees, not radians.

(Problem 3.) x2 + x + 1 = 0 have two complex solutions, a and b.
Find the value of a(28081996+17081945) + b(24031995+1113636363636)

(Problem 4.) If x is a positive real number,
what is the minimum value of xx ?
Express the answer in terms of e (Euler's constant).

Saturday, November 6, 2010

My first trophy...

From left to right: Verdiyanto Saputra, and Ivan Masli (SMAK 1 BPK PENABUR Jakarta), Samuel Wirajaya (me), and Ardyanto Widjojo, the jury, Hendrik L. Medlama, and Regina Chandra (SMAK BPK PENABUR Gading Serpong)

Hello world...
I really miss my own blog...

Last week is one of the best weeks I ever had. Actually, the title should be "my second trophy" but I mean, this is my first trophy since I'm in the senior high school (Sekolah Menengah Atas or SMA in Indonesia).

I registered myself and my partner Ardyanto Widjojo in a physics competition called Einstein Competition, held by Universitas Negeri Jakarta (UNJ). In 24 October, 2010, at UNJ's library hall, me and Ardyanto W. took the selection test. The test was consisted of 40 multiple choice problems.

I was surprised when I heard that I and Ardyanto were in the top 15, and made it to the semifinal test. The semifinal test consisted of problems with short answers, and crosswords about physics concepts. We made it to the first rank! I and Ardyanto was selected to the final test. The finalists (ordered by semifinal score) was:

  1. Ardyanto Widjojo and Samuel Wirajaya, SMAK PENABUR Gading Serpong
  2. Ivan Masli and Verdiyanto Saputra, SMAK 1 PENABUR Jakarta
  3. Hendrik Lewu Medlama and Regina Chandra, SMAK PENABUR Gading Serpong
All of the three was PENABUR students. 2 of my school, another one was from SMAK 1 "smukie" PENABUR Jakarta (one of the best schools in Jakarta). This was a problem, since I and Ardyanto are 10th graders, and "smukie" finalists are 12th graders. (Regina and Hendrik are my schoolmates. They are 10th and 11th grader, respectively), i.e. we were youngest competitors.

In the first part of the test, we beat "the smukiez" by 70 points. In the last seconds, the smukiez gained 90 points by answering a question correctly! My heart beat hard. But Ardyanto and I answered the last correctly, the 100 point question! "Yay! First place!" we shouted. "Sudden death.." said Ivan Masli from smukie.

Extra: We also watched the semifinal for Galileo Competition, physics competition for junior high school students, held in the same place by the same instance. One of the finalist (she's from SMPK 2 PENABUR Jakarta) was a physics master... She always rung the bell, start calculating, and answered the questions. Correctly. Without help from her partner. (By the way, she's cute). And she won the first place.

[Second extra: I got enough money (from the prize) to buy Canon 50mm f/1.8 lens.]

[Third extra: My classmates did demand me and Ardyanto to buy (and pay for) pizzas to celebrate it! Oh no!]