MathDB
Problems
Contests
National and Regional Contests
India Contests
India EGMO TST
India EGMO 2024 TST
2
2
Part of
India EGMO 2024 TST
Problems
(1)
What are those floors doing here?
Source: India EGMO TST 2024/2
12/31/2023
Given that
a
1
,
a
2
,
…
,
a
10
a_1, a_2, \dots, a_{10}
a
1
,
a
2
,
…
,
a
10
are positive real numbers, determine the smallest possible value of
∑
i
=
1
10
⌊
7
a
i
a
i
+
a
i
+
1
⌋
\sum \limits_{i = 1}^{10} \left\lfloor \frac{7a_i}{a_i+a_{i+1}}\right\rfloor
i
=
1
∑
10
⌊
a
i
+
a
i
+
1
7
a
i
⌋
where we define
a
11
=
a
1
a_{11} = a_1
a
11
=
a
1
.Proposed by Sutanay Bhattacharya
algebra
floors
Summation
Egmo tst