ChromaMath

What is ChromaMath

ChromaMath gives you a grid, a number to start from and a number to reach. The purple square in the top-left corner holds your starting value; the pink flag in the bottom-right is the exit. Every other square is an operation with a value attached, colour-coded so you can read the board at a glance: green adds, red subtracts, blue multiplies, amber overwrites the running total with its own number and throws away everything you had.

You walk one square at a time, up, down, left or right, and you may not step on a square twice. The total changes as you go and is shown next to the target at all times. Step onto the flag with the wrong number and the board shakes and pushes you back off it — the walk continues, nothing is lost but the seconds. The grid starts at three by three and grows by one square a side every four levels up to six by six, which is thirty-six squares, one path and a great many wrong turns.

How to play

1. Click or tap a square next to the end of your path to step onto it. Tap the last square of the path again, or press Undo, to step back. The white line shows where you have been, and you cannot cross it — no square is used twice.
2. The colours are the operations: green +, red −, blue ×, amber = (replace the total with this number). The current total sits beside the target at the top of the screen; the level is only won when you reach the flag with the two numbers equal.
3. Endless mode runs on one clock: sixty seconds to start, fifteen more for every level you finish, and the run ends when it reaches zero. The Daily Challenge is five levels, the same five for everyone in the world, with no clock at all.
4. Each level pays 100 points plus a speed bonus of up to 60 — two points come off for every second — so the total on the leaderboard is a mix of how far you got and how quickly you read each grid.

Strategies that work

• Work backwards from the flag. Look at the last square you would have to cross to reach it: if that square is a ×3, the number you need one step earlier is the target divided by three, and that alone rules out most of the board.
• The amber = squares are an escape hatch, not a trap. They wipe the total clean, so a grid that has gone hopelessly wrong is often two steps from being right again — cross an amber square and start the arithmetic from there.
• Multiplication is the only operation that grows the number quickly, so on the bigger grids find the × squares first and decide whether you need them at all. A path that avoids every × is usually the one that can be steered with + and − at the end.
• In Endless the clock is the only enemy: sixty seconds to start and fifteen back for each level. Two points a second is a small penalty, so on a hard grid it costs less to stop and read than to wander and lose fifteen seconds of clock you will not get back.
• Stepping onto the flag with the wrong number does not end the level — it just shakes the board and puts you back. Use it: when you are one square from the exit and unsure, try it, and if it refuses you still have your whole path and can Undo your way to a fork.

A little history

Arithmetic puzzles that hide behind a walk are older than the calculators that made arithmetic cheap. The Königsberg bridges gave us a walk with a rule about crossings; magic squares gave us numbers arranged so that every line agrees; and the twentieth-century puzzle magazines were full of grids where the route mattered more than the sums. What all of them share with ChromaMath is that the difficulty does not come from the arithmetic — every operation here is small enough to do in your head — but from the ordering. Multiplying before you add is a different number from adding before you multiply, and on a six-by-six board the number of orderings is far past counting. The colours are there so that the board can be read as a landscape rather than as thirty-six little sums.

Frequently asked questions