MathDB

Let

f(x)

be a function acting on a string of

0

s and

1

s, defined to be the number of substrings of

x

that have at least one

1

, where a substring is a contiguous sequence of characters in

x

. Let

S

be the set of binary strings with

24

ones and

100

total digits. Compute the maximum possible value of

f(s)

over all

s\in S

. For example,

f(110) = 5

\underline{1}10

1\underline{1}0

\underline{11}0

1\underline{10}

, and

\underline{110}

are all substrings including a

1

. Note that

11\underline{0}

is not such a substring.

Problem Statement