Answer to Problem 1.  The following triangle is mathematically the same as the triangle in Problem 1.
The pattern you found in this triangle is very similar to the Pascal's triangle.
Let's compare our triangle to the well known Pascal's triangle.
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Answer 1
The pattern is very obvious. See the following triangles and fractions in printed with blue color.
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If you are not interested in mathematics, it might be better for you to visit the gallery (Section 5) of our article. You can find beautiful pictures and a movie based on this triangle.