Steven G
Elite Member
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- Dec 30, 2014
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What is the smallest three-digit number such that the sum of its digit is same as the product of the digits?
Here is my work.
Let the three digit number be 100a + 10b +1c. a is not 0 since we want a three digit number. Also b and c are non zero as the sum. a+b+c > 1, while abc will be 0 if b or c is 0.
Therefore the smallest number we can use is 111. Now 11x will not work as the sum is x+2 and the product is x
What about 12X? The sum is 3+x and the product is 2x. Now if 3+x=2x, then x=3. So the smallest number with the desired property is 123.
What is the better way to do this??
Here is my work.
Let the three digit number be 100a + 10b +1c. a is not 0 since we want a three digit number. Also b and c are non zero as the sum. a+b+c > 1, while abc will be 0 if b or c is 0.
Therefore the smallest number we can use is 111. Now 11x will not work as the sum is x+2 and the product is x
What about 12X? The sum is 3+x and the product is 2x. Now if 3+x=2x, then x=3. So the smallest number with the desired property is 123.
What is the better way to do this??