About Milo Marwick
Milo Marwick is the name behind a series of logic puzzle books and this free puzzle site. The site has 3D spatial reasoning puzzles (a daily 3D puzzle game, a daily test, cube nets, counting cubes and mental rotation) and Train Tracks, with a daily puzzle, a library of 140 graded puzzles, printable sheets and a solver. The books are listed on the books page.
How a puzzle is made
- A route. The generator draws a random, winding track from a square on the left edge to a square on the bottom edge, covering roughly a third to three fifths of the grid, and rejects routes that are almost all straights or all curves.
- The numbers. The row and column totals are counted from that route.
- Just enough pieces. An exact solver searches every track that fits the numbers. While it finds more than one, the generator reveals a piece where the alternatives disagree. Then it tries removing each revealed piece again, keeping only those the puzzle cannot do without.
- The fairness check. For Easy, Medium and Hard, a second solver that only knows human techniques must finish the puzzle without searching. If it cannot, the generator adds the piece that helps it most, or starts again.
- A final proof. Before a puzzle is published, the exact solver runs once more from scratch and must find exactly one solution, and an independent checker confirms the answer obeys every rule.
How the 3D puzzles are made
The 3D puzzles follow the conventions of the book THINK IN 3D: solids are stacks of cubes, the views are the top, the front and the left side, thick lines mark every change of depth, and anything the views cannot show is taken to be solid ("hidden means solid").
- A solid. The generator stacks cubes at random on a 3 × 3 or 4 × 4 base, fills in anything the views cannot see, and keeps the solid only if it stands in one piece and uses the whole base.
- A full search. For every question, a solver lists every solid that could have the views shown. A question is kept only if exactly one option fits: one solid for "which solid", one drawing for "missing view", and so on.
- An independent check. Before publishing, a second check re-solves every stored question from its data alone. The current bank of more than 1,100 3D puzzles passes with no failures.
Cube nets are checked by folding the net in software and testing each option against all 24 ways a cube can be turned. Mental rotation shapes are checked to differ from their own mirror image, and counting puzzles to show the top of every stack.
How levels are graded
The level is the hardest technique the human-style solver needed, not just the grid size:
| Level | Grid | Hardest technique allowed |
|---|---|---|
| Easy (Curious) | 6×6 | Solvable with counting, the two-connections rule and the no-loop rule. |
| Medium (Clever) | 8×8 | Mostly counting and the loop rules on a bigger grid; a few puzzles also need the crossing-parity rule. |
| Hard (Devious) | 10×10 | Usually needs a short “what if” test on a single cell or connection. |
| Expert (Milo) | 12×12 | Fewest clues; expect longer chains of reasoning. Still exactly one solution. |
The techniques are explained, with diagrams, on the strategy page.
Why we publish our method
A logic puzzle is only fun if it is fair. Showing how the puzzles are built and checked is our way of promising that every grid here has one answer and that the level on the label means something. If you ever find a puzzle that seems to break that promise, please tell us which one and we will look at it.
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