Enigma 482: Hopscotch
7 January 2019
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From New Scientist #1633, 8th October 1988 [link]
I remember playing a version of hopscotch when I was a child. We used a chalked outline like the one shown, and there were various games we could play on it. The simplest one was to start where shown and throw a pebble towards number 1 and then hop to the pebble: then throw it towards number 2 and hop to it, and so on, finally throwing the pebble towards number 9 and hopping to the pebble. You scored 1 if the pebble landed on the correct number, ½ if it missed by one, ⅓ if it missed it by two, and so on, making 9 the maximum possible total score. You were disqualified if the pebble didn’t land on a numbered square.
When I first tried the game I was pretty hopeless. When throwing at number 1 the pebble went past it. I hopped to the pebble, threw the pebble towards number 2, and continued in this way to complete the game. On no occasion was I standing on the square which I should be aiming at and, apart from when the pebble went past number 1 on my first throw, on only one other occasion did the pebble go too far and go past the square I was aiming at. I ended up with the pebble landing on all the squares from 1 to 9 (albeit in the wrong order) and my score was a whole number.
In what order did I visit the squares?
The issue date of New Scientist that this puzzle was published in falls on a Saturday, the issue date of previous magazines fell on a Thursday, so the date of this issue is 9 days after the date of the previous issue.