MathDB

Two permutations

a_1,a_2,\dots,a_{2010}

and

b_1,b_2,\dots,b_{2010}

of the numbers

1,2,\dots,2010

are said to intersect if

a_k=b_k

for some value of

k

in the range

1\le k\le 2010

. Show that there exist

1006

permutations of the numbers

1,2,\dots,2010

such that any other such permutation is guaranteed to intersect at least one of these

1006

permutations.

Problem Statement