consider the set of Northwestern states or provinces (montana, washington, Idaho, Oregon, Alaska, British Columbia, Alberta) if a person choose one element, show that in three yes or no questions we can determine the element
To demonstrate that we can determine the chosen element from the set of Northwestern states or provinces (Montana, Washington, Idaho, Oregon, Alaska, British Columbia, Alberta) using only three yes or no questions, we should follow a binary search approach. Here's how we can do it:
1. Split the set into two equal parts. Divide it into one group containing three elements and another group containing four elements.
Group 1 (Three elements): Montana, Washington, Idaho
Group 2 (Four elements): Oregon, Alaska, British Columbia, Alberta
2. Ask the first question: "Is the chosen element in Group 1?"
a. If the answer is "Yes," proceed to the next step with Group 1.
b. If the answer is "No," proceed to the next step with Group 2.
3. In the chosen group, split it again into two equal parts. Divide the group into one group containing two elements and another group containing one remaining element.
4. Ask the second question: "Is the chosen element in the first subgroup of the chosen group?"
a. If the answer is "Yes," proceed to the next step with the first subgroup.
b. If the answer is "No," proceed to the next step with the second subgroup.
5. In the subgroup, there will be only two remaining elements. Simply ask the final question: "Is the chosen element [state/province X]?"
a. If the answer is "Yes," then [state/province X] is the chosen element.
b. If the answer is "No," then the remaining element is the chosen element.
By following this approach, using three carefully constructed yes or no questions, we can determine the chosen element from the set of Northwestern states or provinces.