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Hi everyone. Getting to the point, the types of questions that math contests have are not really taught, so to speak, in high school. I was just wondering if anyone had any resources or tips for solving these kinds of questions. For example:

Suppose

- Questions that involve repeating decimals and such ... I have no clue where to start

Four tiles identical to the one shown, with a > b > 0, are arranged without overlap to form a square with a square hole in the middle.

http://img19.imageshack.us/img19/6818/abcxp8.png [Broken]

Determine all positive integers N for which there are odd integers a > b > 0 such that the ratio of the area of the inner square to the area of the outer square is 1:N.

- Geometric problems involving ratios are often confusing as well.

I don't expect anyone to answer the questions (I attempted these questions at a math contest already). I just need some tips for future questions that may ressemble these.

Suppose

*n*and D are integers with*n*positive and 0 ≤ D ≤ 9. Determine*n*if*n*/ 810 = 0.9D59D59D5 ...- Questions that involve repeating decimals and such ... I have no clue where to start

Four tiles identical to the one shown, with a > b > 0, are arranged without overlap to form a square with a square hole in the middle.

http://img19.imageshack.us/img19/6818/abcxp8.png [Broken]

Determine all positive integers N for which there are odd integers a > b > 0 such that the ratio of the area of the inner square to the area of the outer square is 1:N.

- Geometric problems involving ratios are often confusing as well.

I don't expect anyone to answer the questions (I attempted these questions at a math contest already). I just need some tips for future questions that may ressemble these.

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