Question: Substitute numbers for the letters so that the following mathematical expressions are correct.
ABC DEF GHI
--- = IE --- = IE --- = IE
3 6 9
Note that the same number must be used for the same letter whenever it appears.
Answer:
A=2, B=1, C=9, D=4, E=3, F=8, G=6, H=5, I=7
Let's start with GHI = 9 * IE. Note that I appears on both the side. Also, after multiplying IE by 9 the answer should have I at the unit's place. The possible values of IE are 19, 28, 37, 46, 55, 64, 73, 82 and 91; out of which only 64, 73 and 82 satisfies the condition. (as all alphabet should represent different digits)
Now, consider DEF = 6 * IE. Out of three short-listed values, only 73 satisfies the equation. Also, ABC = 3 * IE is satisfied by 73.
Hence, A=2, B=1, C=9, D=4, E=3, F=8, G=6, H=5, I=7
219 438 657
--- = 73 --- = 73 --- = 73
3 6 9