2021 WSMO Accuracy Round Problems/Problem 2

Problem

A fair 20-sided die has faces labeled with the numbers $1,3,6,\dots,210$ . Find the expected value of a single roll of this die.

Solution

Note that the numbers on the die are the first 20 triangular numbers. Thus, the expected value of a single roll of this die is $\frac{1+3+6+\ldots+210}{20}=\frac{\frac{20\cdot21\cdot22}{6}}{20}=\boxed{77}.$

~pinkpig

Page

Toolbox

Search

2021 WSMO Accuracy Round Problems/Problem 2

Problem

Solution