Group, an unfinished puzzle from Simon Tatham's Portable Puzzle Collection

from Simon Tatham's Portable Puzzle Collection

You have found your way to a page containing an unfinished puzzle in my collection, not linked from the main puzzles page. Don't be surprised if things are hard to understand or don't work as you expect.

Link to this puzzle: by game ID by random seed

If you've been reading this message for more than a second or two, then this WebAssembly puzzle doesn't seem to be working in your web browser. Sorry!

More information

Most modern browsers should support WASM. I've had reports of success from:

Firefox 87.0
Chrome 89.0.4389.114
Safari 14.0.3 (16610.4.3.1.7)
Edge 89.0.774.68
Opera 75.0.3969.149

If this puzzle isn't working in one of those browsers (or a later version), check to see whether you have any local configuration that might have turned off WebAssembly completely, or some kind of blocking software that might have prevented the WASM code from being downloaded in the first place.

(For example, in Firefox, it's possible to turn off WASM completely by setting javascript.options.wasm to false in the about:config interface. If you've done that, or something analogous in another browser, this puzzle won't run.)

In other browsers, the problem might be that WebAssembly isn't supported at all (for example, Internet Explorer 11), or that a browser update is needed.

If you think that your browser should support WebAssembly, but this puzzle still isn't running, then please report the problem, including as much diagnostic information as you can find.

In particular, try opening your browser's Javascript error console and then reloading this page, and tell me if it reports any error messages.

Also, if your browser has a network diagnostic tab, try the same experiment, to make sure it is successfully loading both of the auxiliary files group.js and group.wasm.

Fill in the grid with the letters shown to the top and left of it, so that the full grid is a valid Cayley table for a group.

If you don't already know what a group is, I don't really recommend trying to play this game. But if you want to try anyway, the above is equivalent to saying that the following conditions must be satisfied:

Latin square. Every row and column must contain exactly one of each letter.

Identity. There must be some letter e such that, for all a, the letter in row e column a and the one in row a column e are both a. In the default mode, this letter is always e and its row and column are filled in for you; by reconfiguring the game using the Type menu, you can select a mode in which you have to work out which letter is the identity.

Inverses. For every letter a, there must be some letter b (which may sometimes be the same letter as a) such that the letters in row a column b and in row b column a are both the identity letter (as defined above).

Associativity. For every combination of letters a, b, and c, denote the letter in row a column b by d, and the one in row b column c by e. Then the letters in row d column c and in row a column e must be the same.

To place a letter, click in a square to select it, then type the letter on the keyboard. To erase a letter, click to select a square and then press Backspace.

Right-click in a square and then type a letter to add or remove the number as a pencil mark, indicating letters that you think might go in that square.

You can rearrange the order of elements in the rows and columns by dragging the column or row headings back and forth. (The rows and columns will stay in sync with each other.) Also, left-clicking between two row or column headings will add or remove a thick line between those two rows and the corresponding pair of columns (which is useful if you're considering a subgroup and its cosets).