Solution #53: Reverse Multiplication
21,978 is the only such number. Suppose that ABCDE x 4 = EDCBA. Since 4A < 10
and A is even, A = 2. Therefore, E = 8. Note that E x 4 must end in 2.
It follows that B <= 2 because 23 x 4 > 89. In fact, B = 1 because the
two-digit number B2 must be a multiple of 4.
Thus far we have found that 21CD8 x 4 = 8DC12. Observe that D >= 4 and that D8 x 4 ends in 12. Therefore, D = 7. The only possible value of C is 9.
Source: Mathematics Teacher
Categories: Arithmetic, Multiplication, Reasoning
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