Solution

Consider the hundreds digit in lines (3), (4) and (5). We have G + B + carry digit (which is either 0 or 1) = G. Moreover, B cannot be 0. Thus we have B = 9.

As B = 9, we have . Also, the unit digit of  is A. Thus C is not 0, 1, 5, 6. Moreover, A can only be the unit digit of , , ,  or , i.e. 1, 4, 6 or 9. Among these, only C = 2 and A = 4 satisfy the condition that .

Now ABC  C = BEA. It follows that E = 8. Consider the tens digit of lines (3), (4) and (5). The unit digit of H + E is the same as A. Now E = 8, A = 4. Thus H = 6.

Now ABC  D = FAGH, C = 2, H = 6, so D is either 3 or 8. But E = 8, so H = 3. Thus the multiplication is actually 492  32. By actually carrying out the multiplication, we get the answer.

Solution