5

Part of 2014 CHMMC (Fall)

Problems(2)

2014 Fall Team #5

Source:

A teacher gives a multiple choice test to

15

students and that each student answered each question. Each question had

5

choices, but remarkably, no pair of students had more than

2

answers in common. What is the maximum number of questions that could have been on the quiz?

2014 CHMMC Tiebreaker 5 \prod^{\infty}_{n=1} 3^{n/3^n}

Source:

Determine the value of

\prod^{\infty}_{n=1} 3^{n/3^n}= \sqrt[3]{3} \sqrt[3^2]{3^2} \sqrt[3^3]{3^3} ...

RadicalsalgebraCHMMC