How Many Questions?
This variation on Twenty Questions teaches kids a bit of information theory and lets them take a different approach to powers of 2.
First, the kids should be familiar with the regular game of Twenty Questions.
Then, ask as an open-ended question: "Suppose instead of the whole world. you were only allowed to think of certain objects. How many questions would it take to find the right one? What if the questions had to have only yes/no answers?"
Instead of telling the kids if they are right or wrong, try it out. Start with 1 object - it should take 0 questions until you know which one it is! (This this variation, the game is over when you _know_ which object it is, you don't have to ask a final question about the actual object.)
Then go to 2 objects, then 3, 4...we went up to 11 objects, writing down the pattern. Note that sometimes you will get to the answer in less questions, but the idea is how many questions do you need to make _sure_ you know which object it is.
Kids will need to think of good questions that bisect the space into approximately equal groupings. If they can do this, they will find that:
| # Objects | # Questions required to KNOW which one it is |
| 1 | 0 |
| 2 | 1 |
| 3 | 2 |
| 4 | 2 |
| 5 | 3 |
| 6 | 3 |
| 7 | 3 |
| 8 | 3 |
| 9 | 4 |
| 10 | 4 |
| 11 | 4 |
Older kids can understand the rule that it is log base 2 rounded up, but younger kids can still get a good intuitive understanding of the rule of bisecting the space to find things, and how that is a powerful thing to do. This exercise also applies to programming and demonstrates a binary search algorithm. But its simple enough for a 5 year old to do!
