David's POTW Solution
- 1. David’s POTW Solution12/20/09Recommended that you write down the answer on a piece of paper as you read to keep track of variables.
- 2. Solution-Step 1The postcard said: So each letter stands for a number. If you add two, four-digit numbers, such as those represented by the words "SEND" and "MORE," and you wind up with a five-digit number, like "MONEY," then the "M" in the word "MONEY" must be the result of the number 1 being carried over from the addition of S+M. We know that M can't be greater than 1, because you can't carry over a 2 from the addition of "S+M." And we know M can't be zero, otherwise it wouldn't be out front in "MORE" and "MONEY." So M=1
- 3. Step 2-So now we have the “M” in more and money =1Remember that the sum of S+M must be 10, or greater. If it's not, there's nothing to carry over to give us the M in "MONEY." Since we already know that M=1, there are only two choices for S. It can be 9, or it can be 8, if there is a "1" carried over from the sum of "E" and "O" So S= 8 or 9
- 4. Step 3You can either carry a 1 over from the E and O column, or not. That means that the addition in the next column, S+M looks like this: That means, O is either 0 or 1. And we know it can't be 1, because M is one. So O=zero
- 5. Step 4Let's try to use S = 8. Here's what you get: For this to be true, E must be equal to 9, soyou can carry a 1 over to the next column. In that case, the N in MONEY has to be zero. But, wait... we already have a zero, remember? So, this example doesn't work. S can't be equal to 8. Therefore we know S=9
- 6. Step 5We know that E is one less than N, because E+0 =N in the column above, which means that for that column to be true, there must be a carry over of 1 from the "N+R" column. Otherwise, E would be equal to N, and that can't happen.
- 7. Step 6Now, try substituting consecutive numbers for E and N. Try 2 and 3 for E and N. It doesn't work. Try 3 and 4 … those don't work, either. Neither do 4 and 5. But, try 5 and 6... and you get lucky! It works, and you get.... So, R must be equal to 9 or, if 1 is carriedover from D+5, then 8. But, we know that S = 9... So now we know that R=8
- 8. Step 7So, here's what we have now: D must be at least 5, since one needs to be carried over. But, we already have assigned 5, 6, 8 and 9. So D must equal 7
- 9. Step 8Now that you have D=7, 7+5=12 so the “y” in “money” must equal 2. Leaving your equation as:So the answer is that his parents senthim dollars.