You are given 10 cell phones and 10 cell numbers(each number corresponds to one of each of those 10 cell phones), but you don't know which number corresponds to which cell phone. Your task is to label each cell phone with its corresponding number. Using optimal procedures, what is the probability that you will finish the task in exactly 5 attempts?
A single attempt is defined as calling a number from a cell phone.
Hint: The caller's number will be displayed in the cell that is being called.
I think the probability of finishing the task in five attempts is 1.
Choose any phone and dial any number. Label the phone, which is ringing with the number you have just called and label the the phone you have used to make the call, according to the caller display, on the other phone. Put these two phones aside and repeat the process until two phones are left. Choose one and dial one of the numbers. There are two options here. If the second phone rings, you can label each accordingly. If, instead, you get an engaged tone, then you know that the number you are ringing belongs to the phone you are holding and the one remaining phone must have the remaining number. So! Exactly five attempts!
Hope I haven't missed anything! :)