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?
