MathDB
Problems
Contests
International Contests
International Olympiad of Metropolises
2021 IOM
4
4
Part of
2021 IOM
Problems
(1)
Middle school logic problem in international mo
Source: IOM 2021 #4
12/10/2021
Six real numbers
x
1
<
x
2
<
x
3
<
x
4
<
x
5
<
x
6
x_1<x_2<x_3<x_4<x_5<x_6
x
1
<
x
2
<
x
3
<
x
4
<
x
5
<
x
6
are given. For each triplet of distinct numbers of those six Vitya calculated their sum. It turned out that the
20
20
20
sums are pairwise distinct; denote those sums by
s
1
<
s
2
<
s
3
<
⋯
<
s
19
<
s
20
.
s_1<s_2<s_3<\cdots<s_{19}<s_{20}.
s
1
<
s
2
<
s
3
<
⋯
<
s
19
<
s
20
.
It is known that
x
2
+
x
3
+
x
4
=
s
11
x_2+x_3+x_4=s_{11}
x
2
+
x
3
+
x
4
=
s
11
,
x
2
+
x
3
+
x
6
=
s
15
x_2+x_3+x_6=s_{15}
x
2
+
x
3
+
x
6
=
s
15
and
x
1
+
x
2
+
x
6
=
s
m
x_1+x_2+x_6=s_{m}
x
1
+
x
2
+
x
6
=
s
m
. Find all possible values of
m
m
m
.
algebra
logic