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web pages for the Java applets. Previously, those have all been maintained by hand in my website's svn area, which is a bit silly. Now we have a file per puzzle in the 'html' subdirectory which contains the puzzle's name, one or two attributes, and the instructions snippet to go below the puzzle applet; and then there's a Perl script that builds all the real web pages out of that by adding in the parts common across all files: the header, footer, and middle fragment with the <applet> tag and resizing bits and pieces. One piece _not_ checked in here is the footer text specific to my hosting at chiark, which I think does still belong in the www area. So Buildscr doesn't actually build the web pages; it just delivers the bits and pieces by which my nightly snapshot script will be able to run the program that _does_ build them, passing that footer as an extra argument. [originally from svn r9780]
53 lines
2.3 KiB
HTML
53 lines
2.3 KiB
HTML
unfinished:Group
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<p>
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Fill in the grid with the letters shown to the top and left of it, so
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that the full grid is a valid
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<a href="http://en.wikipedia.org/wiki/Cayley_table">Cayley table</a>
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for a
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<a href="http://en.wikipedia.org/wiki/Group_(mathematics)">group</a>.
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<p>
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If you don't already know what a group is, I don't really recommend
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trying to play this game. But if you want to try anyway, the above is
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equivalent to saying that the following conditions must be satisfied:
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<ul>
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<li>
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<strong>Latin square</strong>. Every row and column must contain
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exactly one of each letter.
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<li>
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<strong>Identity</strong>. There must be some letter <i>e</i> such
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that, for all <i>a</i>, the letter in row <i>e</i> column <i>a</i> and
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the one in row <i>a</i> column <i>e</i> are both <i>a</i>. In the
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default mode, this letter is always <i>e</i> and its row and column
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are filled in for you; by reconfiguring the game using the Type menu,
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you can select a mode in which you have to work out which letter is
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the identity.
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<li>
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<strong>Inverses</strong>. For every letter <i>a</i>, there must be
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some letter <i>b</i> (which may sometimes be the same letter
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as <i>a</i>) such that the letters in row <i>a</i> column <i>b</i> and
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in row <i>b</i> column <i>a</i> are both the identity letter (as
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defined above).
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<li>
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<strong>Associativity</strong>. For every combination of
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letters <i>a</i>, <i>b</i>, and <i>c</i>, denote the letter in
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row <i>a</i> column <i>b</i> by <i>d</i>, and the one in row <i>b</i>
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column <i>c</i> by <i>e</i>. Then the letters in row <i>d</i>
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column <i>c</i> and in row <i>a</i> column <i>e</i> must be the same.
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</ul>
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<p>
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To place a letter, click in a square to select it, then type the
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letter on the keyboard. To erase a letter, click to select a square
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and then press Backspace.
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<p>
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Right-click in a square and then type a letter to add or remove the
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number as a pencil mark, indicating letters that you think
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<em>might</em> go in that square.
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<p>
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You can rearrange the order of elements in the rows and columns by
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dragging the column or row headings back and forth. (The rows and
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columns will stay in sync with each other.) Also,
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left-clicking <em>between</em> two row or column headings will add or
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remove a thick line between those two rows and the corresponding pair
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of columns (which is useful if you're considering a subgroup and its
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cosets).
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