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Romania Team Selection Test
1979 Romania Team Selection Tests
6.
Max max of product of binomial coefficients
Max max of product of binomial coefficients
Source: Romanian TST 1979 Day 1 P6
April 15, 2023
algebra
binomial coefficients
Problem Statement
If
n
>
2
n>2
n
>
2
is a positive integer, compute
max
1
⩽
k
⩽
n
max
n
1
+
.
.
.
+
n
k
=
n
(
n
1
2
)
(
n
2
2
)
…
(
n
k
2
)
.
\max_{1\leqslant k\leqslant n}\max_{n_1+...+n_k=n} \binom{n_1}{2}\binom{n_2}{2}\ldots\binom{n_k}{2}.
1
⩽
k
⩽
n
max
n
1
+
...
+
n
k
=
n
max
(
2
n
1
)
(
2
n
2
)
…
(
2
n
k
)
.
Ioan Tomescu
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