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India IMO Training Camp
2012 India IMO Training Camp
3
Number of 6-tuples satisfying conditions
Number of 6-tuples satisfying conditions
Source:
July 17, 2012
Problem Statement
How many
6
6
6
-tuples
(
a
,
b
,
c
,
d
,
e
,
f
)
(a, b, c, d, e, f)
(
a
,
b
,
c
,
d
,
e
,
f
)
of natural numbers are there for which
a
>
b
>
c
>
d
>
e
>
f
a>b>c>d>e>f
a
>
b
>
c
>
d
>
e
>
f
and
a
+
f
=
b
+
e
=
c
+
d
=
30
a+f=b+e=c+d=30
a
+
f
=
b
+
e
=
c
+
d
=
30
are simultaneously true?
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