MT x MT = XYM
If you pay close attention, then you will find that XYM is a 3-digit number and it is the square of a 2-digit number MT.
Now, the maximum value of a 3-digit number is 999.
Therefore, the maximum value of M is 3.
This is true because if you take 4 as the ten’s digit and 0 as the units digit, the number will be 40.
However, 40 x 40 = 1600, which is a 4-digit number. Hence, M cannot be greater than 3.
Therefore, the possible values of M will be 1, 2 or 3 (it cannot be 0 since it is a tens digit).
Next, you will notice that while multiplying MT by itself, the units digit T is multiplied by itself and the resulting square has M as the units digit.
By the property of squares, you know that the square of any number will give 0,1,4,5,6, or 9 as the units digit (check by squaring all the numbers from 0 to 9).
Since M is units digit of the square of T, its value can only be 0,1,4,5,6 or 9.
However, we saw that M cannot be greater than 3 and it cannot be 0.
Therefore, M = 1
Now, of the numbers between 0 to 9, only the squares of 1 and 9 have the units digit as 1.
However, we don’t represent two different numbers by the same alphabet (M and T represent different numbers).
Therefore, T = 9
Therefore, the number is 19 and its square is 361.
MT = 19
XYM = 361