"Across" and "down" are not specified as each letter only corresponds to one answer.
No number begins with zero.
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A is 19 times a square
The product of B's digits is 19 more than their sum
C is a palindrome whose digits add up to 19
D is 19 more than a square
The digits of E add up to 19
F is a square whose digits add up to 19
G is divisible by 19 and is still divisible by 19 when its digits are reversed
H is a cube which is 19 more than a square
The sum of the squares of the digits of I is 19
J is a square which is 19 more than a cube
The sum of the squares of the digits of K is divisible by 19
L is 19 times a square
M is a palindrome which is divisible by 19
N is 19 times a prime
O is a square which is divisible by 19
P is divisible by 19
Q is 19 less than a square
The digits of R add up to 19
The digits of S add up to 19
T is divisible by 19 and its digits add up to 19
U is a square which is divisible by 19
V is 19 times the sum of its digits
W is a prime whose digits add up to 19
X is divisible by 19
Y is 19 times a prime
Z is 19 more than a cube