Here is a new puzzle with moving counters, or coins, that at first glance looks as if it must be absurdly simple. But it will be found quite a little perplexity. I give it in this place for a reason that I will explain when we come to the next puzzle. Copy the simple diagram, enlarged, on a sheet of paper; then place two white counters on the points $1$ and $2,$ and two red counters on $9$ and $10.$
The puzzle is to make the red and white change places.
You may move the counters one at a time in any order you like, along the lines from point to point, with the only restriction that a red and a white counter may never stand at once on the same straight line. Thus the first move can only be from $1$ or $2$ to $3,$ or from $9$ or $10$ to $7.$
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