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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2021 China Second Round A2
2
2
Part of
2021 China Second Round A2
Problems
(1)
combinatorics problem
Source: 2021 China Second Round A2
2/23/2023
Find the maximum value of
M
M
M
, if you choose
10
10
10
different real numbers randomly in
[
1
,
M
]
[1,M]
[
1
,
M
]
, there must be
3
3
3
numbers
a
<
b
<
c
a<b<c
a
<
b
<
c
, satisfy
a
x
2
+
b
x
+
c
=
0
ax^2+bx+c=0
a
x
2
+
b
x
+
c
=
0
has no real root.
combinatorics