Consider the following features of a positive integer N:

a. 3 divides N.

b. 7 divides N.

c. 21 divides N.

d. N ‘s decimal presentation needs exactly 2 distinct digits.

e. N ‘s decimal presentation needs exactly 3 distinct digits.

f. It is less than 30.

g. It is less than 260.

h. It is less than 1000.

i. It is a square number.

j. It is a triangular number.

k. It is a palindrome number.

l. It is a 6-digit number.

m. It is a cube number.

n. The sum of its digits is 9.

o. It is a perfect number.

p. It is a prime number.

Clearly no N fulfills all the above conditions.

Still different numbers may be uniquely defined by some subsets.

Consider subset SB1= (a,b,c,d,f,g,h,j) and SB2= (c,f) .

Although both define uniquely the number 21, only SB2 is void

of redundant statements.

Let's call subsets like SB2 CORE-subsets.

List all numbers that can be uniquely defined

by CORE-subsets of the above list.

Provide a short comment on the puzzle's title.

Rem. Analytical solution preferred.