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KoMaL A Problems
KoMaL A Problems 2017/2018
A. 708
A. 708
Part of
KoMaL A Problems 2017/2018
Problems
(1)
A very strange binary number is rational
Source: KoMaL A. 708
5/21/2023
Let
S
S
S
be a finite set of rational numbers. For each positive integer
k
k
k
, let
b
k
=
0
b_k=0
b
k
=
0
if we can select
k
k
k
(not necessarily distinct) numbers in
S
S
S
whose sum is
0
0
0
, and
b
k
=
1
b_k=1
b
k
=
1
otherwise. Prove that the binary number
0.
b
1
b
2
b
3
…
0.b_1b_2b_3…
0.
b
1
b
2
b
3
…
is a rational number. Would this statement remain true if we allowed
S
S
S
to be infinite?
algebra