2

Part of 2016 Online Math Open Problems

Problems(2)

2015-2016 Spring OMO #2

Source:

x

y

z

be real numbers such that

x+y+z=20

x+2y+3z=16

. What is the value of

x+3y+5z

?
Proposed by James Lin

Online Math Open

2016-2017 Fall OMO Problem 2

Source:

Yang has a standard

6

-sided die, a standard

8

-sided die, and a standard

10

-sided die. He tosses these three dice simultaneously. The probability that the three numbers that show up form the side lengths of a right triangle can be expressed as

\frac{m}{n}

, for relatively prime positive integers

m

n

100m+n

.
Proposed by Yannick Yao