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Lusophon Mathematical Olympiad
2014 Lusophon Mathematical Olympiad
2
2
Part of
2014 Lusophon Mathematical Olympiad
Problems
(1)
IV Lusophon Mathematical Olympiad 2014 - Problem 2
Source:
12/29/2014
Each white point in the figure below has to be completed with one of the integers
1
,
2
,
.
.
.
,
9
1, 2, ..., 9
1
,
2
,
...
,
9
, without repetitions, such that the sum of the three numbers in the external circle is equal to the sum of the four numbers in each internal circle that don't belong to the external circle.
(
a
)
(a)
(
a
)
Show a solution.
(
b
)
(b)
(
b
)
Prove that, in any solution, the number
9
9
9
must belong to the external circle.