Question 176031

In the following addition problem, Y, O, and U are different digits.  Solve the following problem:
<pre><font size = 4 color = "indigo"><b>
I'm going to change the letter "O" to the letter "Q" 
because the letter "O" looks too much like zero.


YOU + YOU + YOU = UUU

Sorry there can't be a solution. Why?

 Y Q U
 Y Q U
 Y Q U
 -----
 U U U

Adding the rightmost column

U + U + U

If there was 0 (nothing) to carry, then

U + U + U = U
       3U = U
       2U = 0
        U = 0

If U were 0, then the next column would be

Q+Q+Q = 0 or Q+Q+Q = 10
   3Q = 0       3Q = 10
    Q = 0        Q = {{{3&1/3}}}  

But Q can't be 0 because U = 0, and it can't be
{{{3&1/3}}} so there had to be 1 to carry.  
Therefore

U + U + U = 10 + U
       3U = 10
        U = 5

So therefore we have:

   1
 Y Q 5
 Y Q 5
 Y Q 5
 -----
 5 5 5

Adding up the middle column with the carry,
we have

1 + Q + Q + Q = 5 or 15
  
1 + 3Q = 5   or   1 + 3Q = 15 
    3Q = 4   or       3Q = 14
     Q = {{{3/4}}}     Q = {{{4&2/3}}}

But Q can't be a fraction, so there
can be no solution.  Sorry.

Edwin</pre>