A lozenge puzzle in disguise

Flat Cube Lab

Twist any little hexagon. The colors travel with the lozenges—and every shape-changing twist secretly adds or removes one cube.

Click = selected direction · right-click or Shift-click = opposite

Solved All 27 lozenges are home.

Solved

0Your turns

0Cubes lifted

0Known way home

Cube size

Twist size

Direction

Scramble strength

So, is it actually hard?

Shape alone: manageable. There are 980 uncolored tilings, and “cubes lifted” is the exact number of shape-changing moves back to this empty-tray target.

With colors: yes. Twists also permute the lozenges without changing the shape. The article’s later update gives an order-3 lower bound of 81 moves and exhibits two states 91 moves apart.

How to read the board

Each white dot is a legal little hexagon. Pick a twist size and direction, then click a dot. Right-click or Shift-click reverses the selected direction. A 60° or 180° twist changes the tiling; 120° only cycles colors.

Read James Propp’s original article ↗