The Game of 21
Inspired by Dave’s recent post at MathNotations, I recently introduced the game of “21” to my intermediate group (approx. 3rd – 5th grade levels). (See the post linked above for rules.) I introduced it in the 2nd half of a class before our February break. I told them to come challenge me when they thought they could beat me. (I went ahead and told the kids that once they figured out all the tricks to the game, whoever went first could guarantee a win, and so when I played against them, I offered to let them go first. ) Usually, after beating their partner a few times in a row, they would conclude that they could beat me, but they couldn’t. 😉 Most of them had started recognizing a few winning (or losing) positions near the end of the game, but only a couple were making methodical notes. By the end of that period, no one had really “solved” the game, though a few (particularly those making notes) were getting there.
We played again Friday. One by one, they started solving it. By the end of the period, about half of them could win consistently if they went first. The others are on their way.
The nice thing about this game is that when someone “solves it” you can just change the game on them, and keep them busy. I sent one pair off with the rule “whoever says 21 wins” and another pair wanted to play to “23” instead. Neither of them made an immediate leap to how to change their strategy for those new conditions. But when they get good at that, we can change the number of numbers they are allowed to play in a turn, etc.
Incidentally, I also taught the game to a pair of 9- and 11-year-old brothers who were driving their mother crazy in the waiting room at Honda’s service department. The 11-year-old was catching on faster than his brother, but still didn’t have the whole thing figured out, so I offered the younger brother that I would beat the older brother on his behalf. 😉 In any case it kept them busy until their car was ready.