MathDB

Let

X

the set of all sequences

\{a_1, a_2,\ldots , a_{2000}\}

, such that each of the first 1000 terms is 0, 1 or 2, and each of the remaining terms is 0 or 1. The distance between two members

a

and

b

X

is defined as the number of

i

for which

a_i

and

b_i

are different. Find the number of functions

f : X \to X

which preserve the distance.

5