MathDB

Consider a random string

s

10^{2020}

base-ten digits (there can be leading zeroes). We say a substring

s'

(which has no leading zeroes) is self-locating if

s'

appears in

s

at index

s'

where the string is indexed at

1

. For example the substring

11

in the string “

122352242411

” is selflocating since the

11

th digit is

1

and the

12

th digit is

1

. Let the expected number of self-locating substrings in s be

G

. Compute

\lfloor G \rfloor

Problem Statement