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Question 1159399: Three + three + four = eleven
Found 5 solutions by josgarithmetic, Alan3354, greenestamps, ikleyn, Edwin McCravy:
Answer by josgarithmetic(39629)   (Show Source):
You can put this solution on YOUR website! That's wrong.
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A question answered from the past was this:
https://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.156440.html
Answer by Alan3354(69443)  (Show Source):
Answer by greenestamps(13208)  (Show Source):
You can put this solution on YOUR website!
The problem is to find solutions to the word arithmetic problem
THREE
THREE
+ FOUR
---------
ELEVEN
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.
And many problems like this are nearly impossible to solve using logical reasoning because they contain too few clues.
This problem is closer to the second case.
(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:
THR11
THR11
+ FOUR
---------
1L1V1N
(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
THR11
THR11
+ FO9R
---------
1L1V1N
(3) After that, there is not much to go on; finding solution(s) involves only trial and error.
I personally would not pursue a manual solution for this problem any further.
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.
Answer by ikleyn(52873)  (Show Source):
You can put this solution on YOUR website! .
See also this web-page:
http://mathforum.org/library/drmath/view/56789.html
Some efforts were made there and some progress was achieved;
but the solution was not completed . . .
/\/\/\/\/\/\/\/
Below is my comment to the Edwin' solution.
In Math problems, if they are posed accurately, we always know, what we are doing, what is our goal,
we always can check, if our solution is correct, and when we complete the solution, we feel ourselves enriched with knowledge.
In puzzle problems, like this one, we don't know what we are doing, what is our goal; we can not check if our solution is correct,
and when we complete a "solution", we are not enriched even for one single milligram of knowledge.
It is why I HATE these puzzles.
They suit for only one purpose: to kill your time.
And their authors make their money this way . . . by killing your time . . .
It is the only meaning of any activity with puzzles: you agree to kill your time for a sake making money to their authors.
Answer by Edwin McCravy(20063)  (Show Source):
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