This goal of this series is to share information on a topic that is a passion of mine: mathematics. There are so many different topics in math to learn and fascinate about. My goal is to create a series of puzzles that share these math topics, and some of their history, while also allowing you to use those skills to solve for the necessary coordinates. The goal is to provide puzzles that aren’t too difficult, but can also offer a challenge.
Pascal’s triangle is a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression. It is named for the 17th century French mathematician Blaise Pascal. However, it is far older than this. Ancient Chinese mathematicians represented this pattern back in the 11th and 13th centuries where it was, at times, referred to as the “Old Method”. It was even studied in the 11th century by Persian mathematician and astronomer, Omar Khayyam.
The triangle can be constructed by placing a 1 along the left and right edges. Then it is filled out from top to bottom by adding together the two numbers just above to the right and left of that position. This can continue infinitely. You can notice in the one image, the exponent increases as well beginning with \(2^0\) which is 1 since any value to the power of 0 is 1. There are numerous patterns and sequences located within, even the Fibonacci sequence!
To find the required coordinates, solve the puzzle below. The coordinates needed lie within.
3, 1, 126, 15, 3, 2
70, 4, 6, 6, 56, 1, 2
Please replace cache exactly as you find it for the next cacher to experience.
Congratulations to LadyCache on the FTF!