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National and Regional Contests
South Africa Contests
South Africa National Olympiad
2017 South Africa National Olympiad
1
1
Part of
2017 South Africa National Olympiad
Problems
(1)
Fraction closest to 1
Source: SAMO 2017 Q1
7/30/2017
Together, the two positive integers
a
a
a
and
b
b
b
have
9
9
9
digits and contain each of the digits
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
1, 2, 3, 4, 5, 6, 7, 8, 9
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
exactly once. For which possible values of
a
a
a
and
b
b
b
is the fraction
a
/
b
a/b
a
/
b
closest to
1
1
1
?
algebra
Fractions