[Computational Complexity] 4/12/2007 11:16:00 AM
I recently visited my nephew and his five kids and tried to get my 8-year-old great nephew Justin interested in some math. I told him that I am thinking of a number between 1 and 100, and he should ask YES/NO questions until he guessed it. Try to ask as few questions as possible. His first three questions were as follows.
- Is it bigger than 20? (YES)
- Is it even? (YES)
- Does it have a 7 in it? (NO)
- Is it 80? (NO)
It took him 20 more questions to get it. I bet him a quarter I could get his number with 10 questions. I succeeded and he had to beg his dad for a quarter. I've been told he has learned not to gamble with Uncle Bill. His father told me that the concept of `try to make every question cut the number of possibilities in half' was over his head since he has not learned fractions yet.
I then tried NIM-games. There are toothpicks on the table and you can remove 1 or 2. The players alternate. The player who removes the last toothpick WINS. He played his sister Jordan (who is nine) with different numbers of toothpicks on the table. They DID catch on that if the number of toothpicks is 3,6,9,12, ... like that, then Player II wins, otherwise Player I wins. They then did NIM with removing 1 or 2 or 3 and also 1 or 2 or 3 or 4, They learned the trick and the pattern. They liked it and learned some math.
I do not know if this is indicative, but it may well be that if a kid has not learned fractions yet, binary search may be over his head, while NIM games is fine and fun.
Warning: I once tried to teach my 6-year old nephew Michael that, when doing multiplication, the order does not matter.
BILL: Say you had two pans of brownies. One is 3 by 5 and the other is 5 by 3. Then---
MICHAEL: Do you! I love brownies!
We didn't get much math done ...
Posted by GASARCH to Computational Complexity at 4/12/2007 11:16:00 AM