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Source: Cono Sur 1992-problem 3

May 29, 2006

algebra unsolvedalgebra

Problem Statement

Consider the set

S

of

100

numbers:

1; \frac{1}{2}; \frac{1}{3}; ... ; \frac{1}{100}

. Any two numbers,

a

and

b

, are eliminated in

S

, and the number

a+b+ab

is added. Now, there are

99

numbers on

S

. After doing this operation

99

times, there's only

1

number on

S

. What values can this number take?

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