This game is about students learning to be systematic, methodical and organized in their reasoning. Tell the students you’re thinking of a number between 1-100. Their task is to determine what your number is using no more than 7 “yes or no” questions. As soon as a student asks, “Is it ___?”, the game is over, right or wrong.
It’s always possible to determine the number in seven steps by asking questions that eliminate half of all remaining numbers. So the first question could be “Is the number between 1-50?” Whether yes or no, half the numbers have been eliminated. Another opening question could be, “Is it an odd number?” Again, half the numbers are eliminated. (Keep a running record on the board or overhead.) The hardest question is the last one if students have narrowed their choices down to two numbers, but it doesn’t have to be a 50/50 guess. There are questions they can ask to determine the number:
If the remaining numbers, for example are 51 and 53 a student could ask, “Can we eliminate 51?” Whether yes or no, they now know the number you selected. Another possible question: “Does your number end in a 1?” Same deal.
When students have mastered this, ask them to figure out the maximum number of questions to ask to determine a number between 1-1000. Surprisingly, only three more questions are needed, for a total of 10.
from:
http://washmath.org/files/GamesAndActivities.pdf