MathDB

p1. A regular

6

-face dice is thrown three times. Calculate the probability that the number of dice points on all three throws is

12

?
p2. Given two positive real numbers

x

and

y

with

xy = 1

. Determine the minimum value of

\frac{1}{x^4}+\frac{1}{4y^4}.

p3. Known a square network which is continuous and arranged in forming corners as in the following picture. Determine the value of the angle marked with the letter

x

. https://cdn.artofproblemsolving.com/attachments/6/3/aee36501b00c4aaeacd398f184574bd66ac899.png
p4. Find the smallest natural number

n

such that the sum of the measures of the angles of the

n

-gon, with

n > 6

is less than

n^2

degrees.
p5. There are a few magic cards. By stating on which card a number is there, without looking at the card at all, someone can precisely guess the number. If the number is on Card

A

and

B

, then the number in question is

1 + 2

(sum of corner number top left) cards

A

and

B

. If the numbers are in

A

B

, and

C

, the number what is meant is

1 + 2 + 4

or equal to

7

(which is obtained by adding the numbers in the upper left corner of each card

A

B

, and

C

). https://cdn.artofproblemsolving.com/attachments/e/5/9e80d4f3bba36a999c819c28c417792fbeff18.png a. How can this be explained? b. Suppose we are going to make cards containing numbers from

1

to with

15

based on the rules above. Try making the cards.
[hide=original wording for p5, as the wording isn't that clear]Ada suatu kartu ajaib. Dengan menyebutkan di kartu yang mana suatu bilan gan berada, tanpa melihat kartu sama sekali, seseorang dengan tepat bisa menebak bilangan yang dimaksud. Kalau bilangan tersebut ada pada Kartu A dan B, maka bilangan yang dimaksud adalah 1 + 2 (jumlah bilangan pojok kiri atas) kartu A dan B. Kalau bilangan tersebut ada di A, B, dan C, bilangan yang dimaksud adalah 1 + 2 + 4 atau sama dengan 7 (yang diperoleh dengan menambahkan bilangan-bilangan di pojok kiri atas masing-masing kartu A, B, dan C) a. Bagaimana hal ini bisa dijelaskan? b. Andai kita akan membuat kartu-kartu yang memuat bilangan dari 1 sampai dengan 15 berdasarkan aturan di atas. Coba buatkan kartu-kartunya

day 2

Problems(1)