** S E N D
+ M O R E
-----------------
= M O N E Y**

** **

Now letter M must be representing the carry generated & it must be 1.

And if M = 1 then S must be 9 or 8 if carry is generated from hundreds place.

In any case, O can be either 0 or 1. But can't be 1 as M = 1 hence O = 0.

If O = 0 then E + 0 = N i.e. E = N if there is no carry from tens place.

Hence, **N = E + 1.**

Let's turn towards tens place now. With no carry from units place N + R = 10 + E .

Putting N = E + 1, we get, R = 9. And with carry from units place, we have,

1 + N + R = 10 + E, gives us R = 8. Hence either** R = 9** and** S = 8** or **R = 8** or** S = 9.**

For a moment, let's assume** R = 9 **and **S = 8 **with **no carry** from units place, then,

8 E N D
+ 1 0 9 E
=========
1 0 N E Y

For this to be correct, we need carry at thousands place generated from hundreds

place. That's only possible if E = 9 and carry is generated from tens place

forwarded to hundreds place. Since 9 is already being used for R this combination

is just impossible.

Hence,** R = 8** and **S = 9** with **carry 1** from units place.

Now it looks like,

9 E N D
+ 1 0 8 E
========
1 0 N E Y

This means** D + E >= 10** i.e. **D + E = 10 + Y.** And numbers left are 2,3,4,5,6,7.

If** E = 2** then D must be 8 or 9 for D + E >= 10.

Since 8 and 9 already taken, this is not possible.

If** E = 3** then D can be 7 but Y would be 0 in the case.

Since O = 0 already taken this value of E is also not valid.

For any other value of D, D + E < 10 .

If **E = 4** then D = 7 or 6 and Y = 0 or 1.

Both are taken hence this value of E in invalid.

Also,D <= 5 in the case gives D + E < 10 .

If** E = 6, N = 7** then, D <= 5.

With D = 5 or 4, Y = 0 or 1, both are used for O and M already.

And for D = 2 or 3,D + E < 10 .

In short, this value of E is also not valid.

So only value of** E **left is** 5**. Hence,** N = 6 **and** D = 7.** That gives, **Y = 2.**

** **

** **

To conclude,

**9 5 6 7
+ 1 0 8 5
=========
1 0 6 5 2 **

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