What am I suppose to do here does anybody know?
Consider the set of northwestern states or provinces {Montana, Washington, Idaho, Oregon, Alaska, British Columbia, Alberta}. If a person chooses one element, show that in three yes or no questions, we can determine the element.
You take a property of these states that can be expressed as a number and such that it is different for all the states, e.g. population size. Then you do a repeted bisection.
You choose a number X such that there are as many states with population size higher than X as there are with population size lower than X. You then ask if the state has a population size that is higher than X.
You then have reduced the set of possible States to half. You then repeat this procedure until you are left with one possible State.
At every step the number of possible State is halved, so you need to do this 3 times.
You could do the same general thing as Count Iblis suggested but instead of finding the populations, you can use letters in the names of the "States". I will show one possible path (note that the way you phrased the question, you can ask a different set of questions based on the outcome of previous questions: in other words, the assignment does not state the you must find only 1 set of 3 questions that works in all possible situations).
1) Does the name of the "State" contain the letter N?
Yes {Montana, Washington, Oregon}
No {Idaho, Alaska, British Columbia, Alberta}
suppose the answer is NO.
2) Does the name of the "state" begin with the letter A?
Yes {Alaska, Alberta}
No {Idaho, British Columbia}
Suppose the answer is "No"
3) Does the name of the "state" contain the letter "B"?
Yes {British Columbia}
No {Idaho}
Actually, there's a more general way.
1) Is the "state" one of the first 3 elements in the set?
Yes {Montana, Washington, Idaho}
No {Oregon, Alaska, British Columbia, Alberta}.
Suppose the answer is no.
2) Is the "State" one of the first 2 elements in the remaining set?
Yes {Oregon, Alaska}
No {British Columbia, Alberta}
suppose the answer is Yes.
3) Is the "state" the first element in the remaining set?
Yes {Oregon}
No {Alaska}
sandra bought 2 1/4pounds of lumbaar at 4.00 a lb. if a 7 percent tax was added, how much did she pay i know answer is $9.63 how did they get the answer
To solve this problem, we need to find a way to narrow down the options by asking yes or no questions. Here's one possible approach to determine the element in three questions:
Question 1: Is the chosen element part of the United States?
- If the answer is "yes", it narrows down the possibilities to {Montana, Washington, Idaho, Oregon, Alaska}.
- If the answer is "no", it narrows down the possibilities to {British Columbia, Alberta}.
Question 2: Is the chosen element an island?
- If the answer is "yes", the only option left is Alaska.
- If the answer is "no" (assuming the answer to question 1 was "yes"), it narrows down the possibilities to {Montana, Washington, Idaho, Oregon}.
- If the answer is "no" (assuming the answer to question 1 was "no"), it narrows down the possibilities to {British Columbia, Alberta}.
Question 3: Does the chosen element begin with a vowel?
- If the answer is "yes" (assuming the previous answers lead to {Montana, Washington, Idaho, Oregon}), it narrows down the possibilities to {Idaho, Oregon}.
- If the answer is "no" (assuming the previous answers lead to {Montana, Washington, Idaho, Oregon}), it narrows down the possibilities to {Montana, Washington}.
By asking these three questions, we have determined the element.