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Chile National Olympiad
2006 Chile National Olympiad
1
1
Part of
2006 Chile National Olympiad
Problems
(1)
2 order list of fractions, sum related problem
Source: Chile Finals 2006 L2 p1
10/3/2022
Juana and Juan have to write each one an ordered list of fractions so that the two lists have the same number of fractions and that the difference between the sum of all the fractions from Juana's list and the sum of all fractions from Juan's list is greater than
123
123
123
. The fractions in Juana's list are
1
2
1
,
2
2
3
,
3
2
5
,
4
2
7
,
5
2
9
,
.
.
.
\frac{1^2}{1}, \frac{2^2}{3},\frac{3^2}{5},\frac{4^2}{7},\frac{5^2}{9},...
1
1
2
,
3
2
2
,
5
3
2
,
7
4
2
,
9
5
2
,
...
And the fractions in John's list are
1
2
3
,
2
2
5
,
3
2
7
,
4
2
9
,
5
2
11
,
.
.
.
\frac{1^2}{3}, \frac{2^2}{5},\frac{3^2}{7},\frac{4^2}{9},\frac{5^2}{11},...
3
1
2
,
5
2
2
,
7
3
2
,
9
4
2
,
11
5
2
,
...
Find the least amount of fractions that each one must write to achieve the objective.
algebra
Fraction