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2021 WSMO Accuracy Round Problems/Problem 2

Revision as of 12:22, 23 December 2021 by Pinkpig (talk | contribs) (Created page with "==Problem== A fair 20-sided die has faces labeled with the numbers <math>1,3,6,\dots,210</math>. Find the expected value of a single roll of this die. ==Solution== Note that...")
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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 $\frac{1+3+6+\ldots+210}{20}=\frac{\frac{20\cdot21\cdot22}{6}}{20}=\boxed{77}.$

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