# Aime 2007 I 10

ehrenfest

## Homework Statement

In a 6 x 4 grid (6 rows, 4 columns), 12 of the 24 squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let be the number of shadings with this property. Find the remainder when is divided by 1000.

There is a picture at this link if you do not understand the question:

http://www.artofproblemsolving.com/Wiki/index.php/2007_AIME_I_Problems#Problem_8 [Broken]

## The Attempt at a Solution

So, somehow we need to divide this into case or find some equivalent problem or something. Symmetry might help us since reflection about the middle horizontal line and reflection about the middle vertical line will preserve the property. Also, inversion of color will preserve the property. So the answer (before you take the remainder) must be a multiple of two. Hmmm...I am out of ideas.

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Homework Helper
erhenfest, the problem has a solution link. Why don't you click it if you are out of ideas? What's the point to posting it here? This is a "Homework Help" forum, I don't think this qualifies.

ehrenfest
erhenfest, the problem has a solution link. Why don't you click it if you are out of ideas?

If there were a hint button, I would click on it but there isn't and I don't want to give up completely.

What's the point to posting it here? This is a "Homework Help" forum, I don't think this qualifies.

Almost none of my questions are homework (in fact I am not even taking any math classes this summer). This is also a "coursework forum". But anyway do you think it would be better to post these in "General Math"?

Homework Helper
That's a reasonable point, but yes, you should probably post them elsewhere. You've already posted one of these without an explicit pointer to the source, though you did quote the AIME reference. Is there a "Problem Practice" forum to discuss problem solving strategies?

Homework Helper
You might try this. Just look at the solution for a little bit. Don't read the whole thing through. That constitutes a hint along the lines to proceed without telling you the whole story. I've done it when practicing.