The puzzle of the 7 coins : The object is to place 7 coins at 7 vertices out of the 8 vertices of the star. When placing any coin you should move it along a free line, and put it down at the end of that line. A line is called free if there is no coin at either of its endpoints.
Suppose that we first put a coin on 1 by moving it along the line 4-1, then a coin on 2, moving along 5-2, next a coin on 3 (along 6-3), a coin on 4 (along 7-4), and a coin on 5 (along 8-5). Then we are played out, because there is no free line left; hence, we can place only five of the seven coins in this way.
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