MathDB

102 Combo

Source: 2018 AIME I #12

March 7, 2018

AMCAIMEAIME I

Problem Statement

For every subset

T

of

U = \{ 1,2,3,\ldots,18 \}

, let

s(T)

be the sum of the elements of

T

, with

s(\emptyset)

defined to be

0

. If

T

is chosen at random among all subsets of

U

, the probability that

s(T)

is divisible by

3

is

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m

.

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