MathDB

Let

S

the set of natural numbers from

1

up to

1001

S=\{1,2,...,1001\}

. Lisandro thinks of a number

N

S

, and Carla has to find out that number with the following procedure. She gives Lisandro a list of subsets of

S

, Lisandro reads it and tells Carla how many subsets of her list contain

N

. If Carla wishes, she can repeat the same thing with a second list, and then with a third, but no more than

3

are allowed. What is the smallest total number of subsets that allow Carla to find

N

for sure?

Problem Statement