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National and Regional Contests
PEN Problems
PEN O Problems
55
55
Part of
PEN O Problems
Problems
(1)
O 55
Source:
5/25/2007
The set
M
M
M
consists of integers, the smallest of which is
1
1
1
and the greatest
100
100
100
. Each member of
M
M
M
, except
1
1
1
, is the sum of two (possibly identical) numbers in
M
M
M
. Of all such sets, find one with the smallest possible number of elements.