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Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
1988 Canada National Olympiad
5
5
Part of
1988 Canada National Olympiad
Problems
(1)
Sequence of positive integers [Canada 1988 - P5]
Source:
10/3/2011
If
S
S
S
is a sequence of positive integers let
p
(
S
)
p(S)
p
(
S
)
be the product of the members of
S
S
S
. Let
m
(
S
)
m(S)
m
(
S
)
be the arithmetic mean of
p
(
T
)
p(T)
p
(
T
)
for all non-empty subsets
T
T
T
of
S
S
S
. Suppose that
S
′
S'
S
′
is formed from
S
S
S
by appending an additional positive integer. If
m
(
S
)
=
13
m(S) = 13
m
(
S
)
=
13
and
m
(
S
′
)
=
49
m(S') = 49
m
(
S
′
)
=
49
, find
S
′
S'
S
′
.