Adapted from Professor Stewart's Casebook of Mathematical Mysteries*
I'll present three puzzles, in stages. Try not to look at the next stage before completing the previous one.
Note that 'a line of four stones' means a line with exactly four stones.
Place twelve stones on a table such that there exist six lines of four stones.
Place twelve stones on a table such that there exist seven lines of four stones.
Move four stones from a certain configuration such that there exist seven lines of four stones. To make the initial configuration, intersect two equilateral triangles to make a six pointed star and put a stone at each intersection of two lines.
*(super duper) highly recommended for anybody who likes mathematical puzzles. Although it is ever so slightly more on the maths side than the puzzle side, there are quite a few enigmas. In fact, there are many other interesting problems and content in the book (e.g insert a mathematical symbol between $4$ and $9$ to make a number between 1 and 10.). I was just wondering if anybody'd be interested in more 'mathematical puzzles' from that book.
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