Cryptarithm: Introduction

What is a cryptarithm?

A cryptarithm (or alphametic) is a kind of mathematical puzzle where the digits in a mathematical equation are substituted by letters or other symbols. Usually, the same letter or symbol should represents the same digit. The solver needs to decode the letters or symbols and find out the encrypted valid equations.

Rule

1. Change all the letters into digits so that the equation becomes valid.
2. The same letters should be the same digits. Different letters should be different digits.
3. The leftmost letter of a "number" cannot be zero (0). Note that the letter "O" does not necessarily represent zero.

Question

Try to solve the 20 puzzles below.

(Scroll down for the answers)

Answer

(If you want to know how the figures are found, feel free to ask in the comment section.)

(1) A=2, B=9, C=11
(2) A=8, B=9
(3) A=1, B=5
(4) A=4, B=9, C=2

(5) A=1, B=9
(6) D=1, O=5, G=3, N=0
(7) D=8, O=2, T=4, N=1
(8) A=9, I=8, O=1, H=5

(9) B=1, O=0, W=2, D=3, G=4
(10) M=1, O=9, G=3, W=8
(11) T=9, L=1, C=8
(12) D=8, I=7, N=2, O=4

(13) G=2, O=6, D=3, I=4, S=1, L=5, O=6, V=7, E=8
(14) H=3, O=2, T=4, D=6, G=7, B=9, U=5, N=1
(15) A=2, B=3, C=5, D=1, X=0
(16) A=7, B=8, C=4, D=2, E=1, F=0, G=9

(17) J=6, O=5, H=1, N=2, Y=0, B=4, E=7, G=8, D=9
(18) E=6, A=2, T=7, G=1, I=5, N=4
(19) L=2, O=1, V=8, E=6, R=4, A=3
(20) W=8, O=7, F=6, D=1, G=5, Y=2