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2020 BMT Individual Tiebreaker 2

Source:

January 9, 2022
combinatoricsalgebra

Problem Statement

Let η∈[0,1]\eta \in [0, 1] be a relative measure of material absorbence. η\eta values for materials combined together are additive. η\eta for a napkin is 1010 times that of a sheet of paper, and a cardboard roll has η=0.75\eta = 0.75. Justin can create a makeshift cup with η=1\eta = 1 using 5050 napkins and nothing else. How many sheets of paper would he need to add to a cardboard roll to create a makeshift cup with η=1\eta = 1?
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