So, let we go to find the word represented by 925764.

Solution:

T+H cannot be 9. Otherwise, A & E both are 1 [which contradicts (1)] or one of A & E is zero [which contradicts (2)]. So, T+H is 8 and 1 is carried from A+E.

Then T cannot be:

0 –[[2]]

2 or 7 – then G & T would be the same digit, contradicting [1]

4 — since , H would then be 4, contradicting [1].

So the possible digits for T & H are as follows:

Then, continuing the table with G, so that G+T is 4 or 14:

Because 1 is carried from A+E, A+E is either 11 or 12.

Suppose, A+E is 11. Then using [[1]] to continue the table with A and E: [ represent cases.]

Suppose A+E is 12. Then by using [1] to continue the table with A and E

Then, keeping [1] & [2] in mind, to continue the table with N, so that N+E is 6 or 16 ( if G+T 10; those case that are not listed are eliminated because no digit is possible for N):

Again, using (1) and (2) to continue the table with M and L so that M+L is 4 or 5 (if A+E=12) , or 14 or 15 (if A+E =11; those cases are not listed are eliminated because no digits are possible for M and L):

Again continuing the table with I , so that I+M is 7 or 17 (if N+E 10; those cases not listed are eliminated because no digits are possible for I), there remains only one case with two sub-cases :

Out of which only is correct since M+L = 14 .

Substituting the letters for the digits is .

Note

• This problem requires handy exercise, and this should be done manually with great concentration.

• I am not good in latex, hence was unable to make perfect matrices. Sorry! Hope you’ll compromise with it.