MathDB

Consider the

10

-digit number

M=9876543210

. We obtain a new

10

-digit number from

M

according to the following rule: we can choose one or more disjoint pairs of adjacent digits in

M

and interchange the digits in these chosen pairs, keeping the remaining digits in their own places. For example, from

M=9\underline{87}6 \underline{54} 3210

by interchanging the

2

underlined pairs, and keeping the others in their places, we get

M_{1}=9786453210

. Note that any number of (disjoint) pairs can be interchanged. Find the number of new numbers that can be so obtained from

M

Problem Statement