MathDB

Given a set

A

of positive integers, the set

A'

is composed from the elements of

A

and all positive integers that can be obtained in the following way: Write down some elements of

A

one after another without repeating, write a sign

+

-

before each of them, and evaluate the obtained expression. The result is included in

A'

. For example, if

A = \{2,8,13,20\}

, numbers

8

and

14 = 20-2+8

are elements of

A'

. Set

A''

is constructed from

A'

in the same manner. Find the smallest possible number of elements of

A

, if

A''

contains all the integers from

1

40

Problem Statement