MathDB

Problem 1. Andi, Beni, Coki, Doni, and Edo are playing truths and lies. Each player becomes a mousedeer or a wolf (This expression is a bit common in Indonesian). A mousedeer always tells the truth, whereas a wolf always lies. Andi says that Beni is a mousedeer. Coki says Doni is a wolf, while Edo says Andi is not a wolf. Beni says Coki is not a mousedeer, Doni says that Edo and Andi are different animals ("mousedeer" and "wolf" are animals). Determine the number of wolves in the game.
Problem 2. Determine all integers

a

and

b

such thar

\frac{\sqrt{2} + \sqrt{a}}{\sqrt{3} + \sqrt{b}}

is a rational number.
Problem 3. Points

P

and

Q

are the midpoints of edges

AE

and

CG

(respectively) on cube

ABCD.EFGH

. If the length of an edge of the cube is 1 unit, determine the area of quadrilateral

DPFQ

.
Problem 4. Prove that

999! < 500^{999}

.
Problem 5. Three points are located on an area bounded by the

Y

-axis and the graph of the equation

7x - 3y^2 + 21 = 0

. Prove that at least two (a pair) of the three points have a distance of less than 4 units from each other.

Problem Statement