06.11.2014

## Find the numbers 6 walkthrough

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When you look at Pascal's Triangle, find the prime numbers that are the first number in the row.

Each row represent the numbers in the powers of 11 (carrying over the digit if it is not a single number). Catalan numbers are found by taking polygons, and finding how many ways they can be partitianed into triangles. These numbers are found in Pascal's triangle by starting in the 3 row of Pascal's triangle down the middle and subtracting the number adjacent to it. For example, if you are expanding (x+y)^8, you would look at the 8th row to know that these digits are the coeffiencts of your answer.

This can be done by starting with 0+1=1=1^2 (in figure 1), then 1+3=4=2^2 (figure 2), 3+6 = 9=3^2 (in figure 1), and so on. Since 10 has two digits, you have to carry over, so you would get 161,051 which is equal to 11^5.

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