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4
2013 Team #4: Sum of real numbers
2013 Team #4: Sum of real numbers
Source:
February 18, 2013
floor function
Problem Statement
Let
a
1
a_1
a
1
,
a
2
a_2
a
2
,
a
3
a_3
a
3
,
a
4
a_4
a
4
,
a
5
a_5
a
5
be real numbers whose sum is
20
20
20
. Determine with proof the smallest possible value of
∑
1
≤
i
≤
j
≤
5
⌊
a
i
+
a
j
⌋
.
\displaystyle\sum_{1\le i \le j \le 5} \lfloor a_i + a_j \rfloor.
1
≤
i
≤
j
≤
5
∑
⌊
a
i
+
a
j
⌋
.
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