Fibonacci Challenge

The fibonacci challenge is inspired by Fibonacci tilings, it allows to touch the mystery of the fibonacci sequence that fascinated mathematicians so much. Fibonacci tilings: The Fibonacci sequence is maybe the most famous arithmetic sequence in mathematics. By definition, the first two numbers in sequence are 1 and 1, and every number after the first two is the sum of the two preceding ones: 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144 … We can construct a square tiling with squares whose side lengths are successive Fibonacci numbers. The Fibonacci spiral is an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling. Fibonacci numbers appear unexpectedly often in mathematics, so much that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms. Artists and Architects were fascinated by the Fibonacci sequence because it is relied to the golden number which is believed to represent aesthetici. The Fibonacci Sequence also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts. The Game: The objective of the game is to construct 7 successive Fibonacci square tiling by colliding consecutives Fibonacci square numbers (F1=1, F2=1, F3=2, F4=3, F5=5, F6=8, F7=13, F8=21, F9=34, F10=55, F11=89, F12=144). Each Square tiling is formed by 5 of consecutive Fibonacci squares plus an origin to design previous Fibonacci numbers. The 7 successive Fibonacci square tiling allow to progress in the Fibonacci sequence until the Fibonacci number 144. A best score is achieved if the user reaches the maximum Fibonacci square number (144) with a minimum of collisions. There is three degree of difficulties in the game: • Beginner: When a Fibonacci square number ( Fn) collide with another one with the value (F(n-1)) the two squares disappear and give birth to a Fibonacci square of value (F(n+1)) • Easy : When a Fibonacci square number ( Fn) collide with two squares with the values (F(n-1)) and (F (n-1)) the squares disappear and give birth to a Fibonacci square of value (F(n+1)) • Difficult: We progress in the Fibonacci sequences when we cover two edges of a given square by a tiling of its two previous square Fibonacci numbers. NB: when two squares with the same value collide, they give the next Fibonacci number if they have the minimum in the considered tiling or disappear if not. The score count the number of collision and the percentage of collision conducting to a progression in the Fibonacci sequence. A percentage with a range of 50% or above is considered good. A score of 60 or above is considered to be excellent.