Warning: before seeing the solutions (below), you may really want to try to see whether you can figure these out by yourself. I found it fun. It is not that much fun to see the completed solution.

Hilmar.

>I plan to post the answers to these on monday.
>
>
>1) Can the following expression be simplified?
>
>

>(x-a)(x-b)(x-c)...(x-z)
>

>
>Only basic algebra is required.
>
>
>In the following problems, each letter represents a digit. Same letter, same digit. Different letters mean different digits.
>
>
>2.
>

>ABCD
>x  4
>----
>DCBA
>

>
>
>3.
>

> SEND
>+MORE
>-----
>MONEY
>

>
>
>Regards, Hilmar.

The answers, as promised. I will leave some blanks, to give you another chance to figure out the solution.

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1. Since one of the terms is (x-x) = 0, the product is zero.

2.

The reasoning, to figure this one out, starts something like this: the first "A" can only be 1 or 2 (3000 x 4 is a five-digit number). The second "A" has to be even, because of the multiplication by 4. The second "D" can only be 8 or 9. The first "D" can't be 9, because 9 x 4 doesn't end with 2. ... etc.,; the complete solution is:

 2178
x   4
-----
 8712

3. Here, the reasoning is a little more complicated. The first "M", of course, can only be 1. From there, it starts getting a little more complicated.

The solution:

 9567
+1085
-----
10652