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Operations

Source: Brazil MO 2018 Grades 8 and 9

November 17, 2018

combinatorics

Problem Statement

One writes, initially, the numbers

1,2,3,\dots,10

in a board. An operation is to delete the numbers

a, b

and write the number

a+b+\frac{ab}{f(a,b)}

, where

f(a, b)

is the sum of all numbers in the board excluding

a

and

b

, one will make this until remain two numbers

x, y

with

x\geq y

. Find the maximum value of

x

.

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