Six cards are numbered 1, 2, ..., 6. Bartek takes some of them. Alek asks Bartek: 

 • How many of the numbers 2, 3, 4, 5, 6 do you have?

 • How many of the numbers 1, 3, 4, 5, 6 do you have?

 • How many of the numbers 1, 2, 4, 5, 6 do you have?

 • How many of the numbers 1, 2, 3, 5, 6 do you have?

 • How many of the numbers 1, 2, 3, 4, 6 do you have?

Bartek responds 4 to all of these questions. What is the sum of the numbers Bartek has?