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The Obliterated Multiplication

Stu Den did a multiplication problem on his paper, but then some ink spilled on it, obliterating all but 5 digits, as shown. The obliterated digits are indicated by *'s.

         2 * *
       x 3 * *
         5 * *
       * 4 * *
     * * 3 * *
     * * * * *
Help Stu out by reconstructing all of the digits. Is their a unique answer?

Hint: Stu remembers that the digit 7 does not occur anywhere in the calculation.

 

Source: Adapted from J. Hunter's Fun With Figures, 1956


Hint: As a start, you are multiplying a number in the 200's by a single digit and getting a number in the 500's. What can you conclude?

 


Solution Commentary: One possibility is 281 x 332 = ....

Can you find others...or "prove" that no other possibilities exist?