document.write( "Question 1159399: Three + three + four = eleven \n" ); document.write( "
Algebra.Com's Answer #782461 by greenestamps(13209)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The problem is to find solutions to the word arithmetic problem
\r\n" );
document.write( "    THREE\r\n" );
document.write( "    THREE\r\n" );
document.write( "  +  FOUR\r\n" );
document.write( " ---------\r\n" );
document.write( "   ELEVEN

\n" ); document.write( "This kind of problem can be good for getting some mental exercise, using logical reasoning and elementary arithmetic to determine which letters represent which digits.

\n" ); document.write( "And many problems like this are nearly impossible to solve using logical reasoning because they contain too few clues.

\n" ); document.write( "This problem is closer to the second case.

\n" ); document.write( "(1) Adding two 5-digit numbers and one 4-digit number and obtaining a 6-digit sum means the leading digit of the 6-digit sum has to be 1. So the problem now looks like this:
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document.write( "    THR11\r\n" );
document.write( "    THR11\r\n" );
document.write( "  +  FOUR\r\n" );
document.write( " ---------\r\n" );
document.write( "   1L1V1N

\n" ); document.write( "(2) The only good clue remaining is the sum in the tens column: 1 plus 1 plus U, plus possibly a carry from the ones column, yields digit 1 in the sum. Logical reasoning tells us that U has to be 9. Now the problem is
\r\n" );
document.write( "    THR11\r\n" );
document.write( "    THR11\r\n" );
document.write( "  +  FO9R\r\n" );
document.write( " ---------\r\n" );
document.write( "   1L1V1N

\n" ); document.write( "(3) After that, there is not much to go on; finding solution(s) involves only trial and error.

\n" ); document.write( "I personally would not pursue a manual solution for this problem any further.

\n" ); document.write( "There are cryptarithmetic solvers you can find online that will find all the solutions to any problem like this in only a second or two.

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