What changes when the board is round
Cross-math is built from cells joined by operators and equals. You place number tiles so that every equation reads true at the same time. Every Lattice board is machine-proven to have exactly one solution, so you never need to guess, and difficulty is graded from Easy to Master by how deep the deduction runs.
Orbits and Dials keep those rules and change the shape. Instead of rows and columns, numbers sit in concentric rings around a central hub. Equations travel two ways at once: around each ring, and inward along the spokes toward the hub. The math is the same. What moves is the way a cell is held in place.
Orbits: rings of numbers around a hub
In Orbits you place tiles, just as you would on a square board, but the geometry is circular. A ring is a closed loop of cells, and a spoke is a line of cells running from the outer edge inward to the hub.
The effect is that every cell answers to two short equations at once: the one that curves around its ring, and the one that runs along its spoke. Where they cross is where a number is pinned. A square grid does something similar with rows and columns, but the round layout makes the double constraint easy to see. Follow a ring and a spoke, and the cell they share is rarely free.
Treat each spoke and each ring as its own small equation. Then look for the most constrained intersection, the cell where one ring and one spoke leave the fewest options. Solve there first. Each value you fix tightens the loops and spokes that pass through it, and the next constrained cell tends to appear nearby.
Dials: twist the rings into truth
Dials is an arcade mode of thirteen levels, and it works the other way around. You do not place tiles. The numbers are already there, set into concentric rings, and you rotate those rings so the values line up along the spokes.
Each spoke is an equation waiting to be made true. As you turn a dial, every number on that ring slides to a new spoke, so one rotation changes many equations at once. The puzzle is alignment rather than filling: you are turning the dials until every spoke reads as a true equation.
Working one spoke at a time
Because a single ring passes through every spoke it touches, you cannot fix one equation in isolation. The move is to find the tightest spoke, the one with the fewest rotations that could satisfy it, and lock that rotation first.
Then trace what it forces. With one ring committed, the numbers it carries are decided for every spoke it crosses, which narrows the choices on the rings still free to turn. Read those neighbours, find the next spoke that is now nearly settled, and continue. You are not spinning at random. You are letting one solved spoke hand you the next.
Reading both worlds well
Orbits and Dials reward the same habit from opposite directions. In Orbits you search for the intersection that is most constrained and build outward from it. In Dials you search for the spoke that is most constrained and let its rotation cascade.
Either way, the round board never asks you to guess. The single proven solution is still there, and the circular shape simply gives you a second axis to read. Trust the tightest equation in front of you, fix it, and let the rings and spokes carry the deduction the rest of the way.