3

Part of 2017 AIME Problems

Problems(2)

Wot n' Summation

Source: 2017 AIME I #3

For a positive integer

n

d_n

be the units digit of

1 + 2 + \dots + n

. Find the remainder when

\sum_{n=1}^{2017} d_n

1000

Catcher in the Right Triangle

Source: 2017 AIME II #3

A triangle has vertices

A(0,0)

B(12,0)

C(8,10)

. The probability that a randomly chosen point inside the triangle is closer to vertex

B

than to either vertex

A

C

can be written as

\frac{p}{q}

p

q

are relatively prime positive integers. Find

p+q