# Is there a better way to solve this?

#### Jomo

##### Elite Member
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??

#### Otis

##### Senior Member
… What is the better way to do this? …
Register a new username, and trick Denis into writing one of his looper programs.
$\;$

#### Otis

##### Senior Member
… What is the better way to do this??
Jomo, to be serious (for a change), I think that your approach is very good. Are you really looking for something better?

I often cringe in mathematics, when I hear statements like "better" or "easier" used to describe alternatives. I mean, this can be very subjective. Sometimes, people use these words not because they can demonstrate a clear advantage; it's just their way of phrasing a personal preference for one way over another. In other words, an alternative may not be better or easier; it's just different.

So, if you're really asking for opinions about what others think is "better", then I'll need to wait for other methods to appear before I can comment about that.

Cheers

#### Jomo

##### Elite Member
Register a new username, and trick Denis into writing one of his looper programs.
$\;$
Denis would write one of his looper program for me without using a different user name. Why do you think otherwise?

#### Otis

##### Senior Member
Denis would write one of his looper program for me without using a different user name. Why do you think otherwise?
I was not being serious.

#### Denis

##### Senior Member
Denis would write one of his looper program for me without using a different user name.
YESSSS...after receipt of my usual fee (Canadian funds)....

#### topsquark

##### Full Member
Take a chess board and place a penny in one of the corners. Then place 2 pennies in the next square, 4 in the next, etc. doubling each time. Fill the chess board. The fee is all the money on the board.

I tell my students that this is what it takes to bribe me to give them an A. They always seem to think it's around 200 dollars.

I also tell them I can put them on a payment plan, with just a one percent interest fee compounded monthly and their children and grandchildren, etc. can support my family for eternity.

-Dan

#### Jomo

##### Elite Member
Take a chess board and place a penny in one of the corners. Then place 2 pennies in the next square, 4 in the next, etc. doubling each time. Fill the chess board. The fee is all the money on the board.

I tell my students that this is what it takes to bribe me to give them an A. They always seem to think it's around 200 dollars.

I also tell them I can put them on a payment plan, with just a one percent interest fee compounded monthly and their children and grandchildren, etc. can support my family for eternity.

-Dan
I'd be willing to accept just the money on the last square