'Circle of Squares' programming challenge
by dogpatch from LinuxQuestions.org on (#5GAE3)
In his Amazing Circle thread, igadoter presented us with a circle of data consisting of the numbers 1 thru 32. The amazing part was that each adjacent pair of numbers when summed yielded a perfect square. He asked for a programmatic way to verify that the conditions were met for the particular sequence of 32 numbers that he supplied, which program was offered by danielbmartin. Others, including myself, have wondered about the possibility of programmatically generating such an amazing circle of numbers, so I hereby issue the programming challenge. Here are the rules:
1. The data must be a logical circle or ring of data, in which there is no defined first and last element, and no defined direction or flow (can be clockwise or counter-clockwise);
2. Each element in the ring must be within the defined limits. In this case, between 1 and 32, with each number occurring exactly once (in any order).
3. Each adjacent pair of numbers must sum to a perfect square. [1, 4, 9, etc] 'Adjacent pair' is defined per rule #1 above. That is, if you define the ring as a linear array, the array must 'wrap around' so that the first and last elements are considered logically adjacent.
Let's have a little fun with this, and, as others have suggested, maybe carry it further than limits of 1 to 32.
1. The data must be a logical circle or ring of data, in which there is no defined first and last element, and no defined direction or flow (can be clockwise or counter-clockwise);
2. Each element in the ring must be within the defined limits. In this case, between 1 and 32, with each number occurring exactly once (in any order).
3. Each adjacent pair of numbers must sum to a perfect square. [1, 4, 9, etc] 'Adjacent pair' is defined per rule #1 above. That is, if you define the ring as a linear array, the array must 'wrap around' so that the first and last elements are considered logically adjacent.
Let's have a little fun with this, and, as others have suggested, maybe carry it further than limits of 1 to 32.