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The postcard said:

And the question is:

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." (How many numbers do you know that start with 0? We rest our case!)

Remember 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"

You 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, what? O is either 0 or 1. And we know it can't be 1, because M is one.

Here's where it gets really interesting. Let's try to use S = 8.

Here's what you get:

For this to be true, E must be equal to 9, so you 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.

We 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.

Now, 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 carried over from D+5, then 8. But, we know that S = 9...

So, 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.

Ready for the final equation? Great! It's....

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