2

Part of 2010 AIME Problems

Problems(2)

Many 9s Product

Source: AIME 2010I Problem 2

Find the remainder when

9 \times 99 \times 999 \times \cdots \times \underbrace{99\cdots9}_{\text{999 9's}}

1000

modular arithmeticAMC

Probability in Square

Source: AIME 2010II Problem 2

P

is chosen at random in the interior of a unit square

S

d(P)

denote the distance from

P

to the closest side of

S

. The probability that

\frac15\le d(P)\le\frac13

\frac{m}{n}

m

n

are relatively prime positive integers. Find m\plus{}n.

probabilitynumber theoryrelatively primeAMC