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National and Regional Contests
PEN Problems
PEN O Problems
26
26
Part of
PEN O Problems
Problems
(1)
O 26
Source:
5/25/2007
A set of three nonnegative integers
{
x
,
y
,
z
}
\{x, y, z \}
{
x
,
y
,
z
}
with
x
<
y
<
z
x<y<z
x
<
y
<
z
is called historic if
{
z
−
y
,
y
−
x
}
=
{
1776
,
2001
}
\{z-y, y-x\}=\{1776,2001\}
{
z
−
y
,
y
−
x
}
=
{
1776
,
2001
}
. Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.
algorithm