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.