Square-Sum Cycle
& Open-Path Generator
Arrange every integer in an interval so each neighboring pair has a perfect-square sum. If a closed circle is impossible, the generator automatically looks for a complete open path.
Enter an interval. A closed cycle is checked first, then an open path.
What the open diagram means
A closed cycle must also make the last and first numbers sum to a square. An open path verifies only the consecutive pairs shown. Its two endpoints have a visible gap, with no sum box and no connector across that gap.
numbers square sums thin lines indicate the contributing pair