Sheet
Show the answers here
Printing gives you two pages. The first has the six puzzles with room to work, and the second has the answers, so you can hand out the puzzles and keep the key. Both pages fit on A4 and on US Letter. If you'd rather keep a file, choose Save as PDF in the print window.
Every sheet has a short code, shown above and in the address bar. Bookmark the page or send someone the link and the same six puzzles come back. That helps when you print a sheet for a class today and want its answers again next week.
What's on a sheet
By default you get one of each: a binary puzzle, a Futoshiki, a Queens board, a star battle, a code breaker and a matchstick equation. If you like one kind best, pick six of it instead. The level mostly changes the size of the board:
| Puzzle | Easy | Medium | Hard |
|---|---|---|---|
| Binary puzzle | 6x6 | 8x8 | 10x10 |
| Futoshiki | 4x4 | 5x5 | 6x6 |
| Queens | 6x6 | 8x8 | 9x9 |
| Star battle | 8x8 | 8x8, with a squeeze | 10x10 |
| Code breaker | 3 digits | 4 digits | 5 digits |
| Matchstick | Single digits | A sign has to change | Numbers up to 29 |
There are 24 boards of each kind at each level, 432 in all. New sheet deals a random six from them, and the level buttons and the menu deal a new sheet too.
How each puzzle works
Binary puzzle
Fill every cell with 0 or 1. Each row and each column has as many 0s as 1s, and three of the same can never sit side by side. An = between two cells means they match, and an × means they differ.
Start with pairs. Two 0s next to each other mean the cells at both ends are 1s. Then look for gaps: a cell between two of the same symbol has to be the other one. The binary puzzle page has all six steps with examples, and boards to play on screen.
Futoshiki
Write the numbers 1 to 4, 5 or 6, depending on the size, once in every row and every column. The little signs between cells are greater than and less than signs, and each one points at the smaller number.
The signs tell you more than they seem to. A cell that a sign points at can't hold the biggest number, and the cell on the open side can't be 1. Chains narrow things fast. If three cells climb in a row, like a < b < c, the bottom one is at most 4 on a 6x6 board. The Futoshiki page walks through the five techniques.
Queens
Place one queen in every row, every column and every region, the shapes marked by thick lines. No two queens may touch, not even at a corner.
Go to the smallest region first. If a region sits entirely inside one row, that row's queen belongs to the region, and you can cross out the rest of the row. On paper, mark ruled out cells with a small dot. You'll use them far more often than the queens. The Queens page explains the rest of the techniques on a board with hints.
Star battle
The same idea with two of everything: two stars in every row, column and region, and no two stars touching, not even at a corner.
Count stars, not cells. If two regions sit entirely inside the same two rows, they use up all four stars of those rows, so every other cell in those rows is empty. Every Medium board needs a squeeze like that at least once, which is why it's harder than Easy at the same size. More on the star battle page.
Code breaker
Each puzzle hides a code of 3, 4 or 5 digits, and no digit appears twice. A code can start with 0. Every row is an old guess with two numbers: how many of its digits are in the code at all, and how many of those sit in the right place.
Start with any guess that scores 0. Cross its digits out everywhere, then go back to the other guesses with fewer digits to worry about. The code breaker guide solves three puzzles step by step, and there's a fixed set of twenty with worked answers on the printable code breaker page.
Matchstick
Each equation is wrong as printed. The digits are made of matches, like a digital clock, and a plus is one flat match with one upright match. Move exactly one match so the equation becomes true. You can't throw a match away or add one.
Look at the signs early. Take the upright match out of a plus and it becomes a minus, and that spare match can turn a 5 into a 9 or a 6 into an 8. If you'd rather work them on screen, there are 30 matchstick puzzles to play.
How the boards are checked
The puzzles come from the generators in my Android games, rewritten to run on this site: binary from Sun and Moon, Futoshiki from Futoshiki, Queens from Queens, code breakers from Crack the Vault and matchsticks from Matchstick Puzzle. Star battle isn't in an app. I wrote its generator for the star battle page.
A board only goes into the pool if a step by step solver can finish it without guessing. It's the same solver that writes the hints on the play pages, so every board can be done with a pencil and some patience.
Then, every time I build the site, a second program that I wrote separately solves every board again by brute force. It has to find exactly one answer, and that answer has to match the key. For the code breakers it tries every possible code: 720 with 3 digits, 5,040 with 4 and 30,240 with 5. For the matchsticks it tries every single match move. If one board fails, the site doesn't build.
What isn't measured is how hard a board feels. Levels follow the size and the steps a board needs, so two Medium boards can still take you very different times.
Printing tips
- Black and white printers are fine. The regions in Queens and star battle are marked by thick lines, and the colors only help.
- The print window may offer to print only some pages. Choose page 1 for the puzzles alone, or page 2 when you only need the key.
- Each page has the sheet code at the top, so a stray answer page always matches its puzzles.
Questions
Can I use these in class?
Yes. Print as many copies as you like for a class, a club or a puzzle night. The answers come out on their own page, and the sheet code lets you print the same set again later.
Is there really only one answer to each?
Yes. Every board was solved by brute force when the site was built, and each one has exactly one answer. That answer is the one in the key.
Which one should I start with?
Matchstick and the 3 digit code breaker are quick. If you've never seen a grid puzzle, try an Easy Futoshiki or binary puzzle next. I find star battle the hardest of the six at every level.
Can I play these on screen instead?
Each kind has its own page with boards and hints: binary, Futoshiki, Queens, star battle, the daily code breaker and matchsticks.
Queens
680 Queens boards from 5x5 to 11x11, a daily board, and hints that explain every step.