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.

(In reply to re(2): Solution? by Charlie)

Isn't it a bit more complicated than this? You can still figure out all of the numbers in five tries even if you call yourself on the first, second, third or fourth try.

For example:

Attempt #1: I call phone 1 from phone 1. Oops.

Attempt #2: I call phone 2 from phone 3.

Attempt #3: I call phone 4 from phone 5.

Attempt #4: I call phone 6 from phone 7.

Attempt #5: I call phone 8 from phone 9. I also know that the number for phone 10 is the one left over.

Does this change the odds at all?

People who are better at probability math than I am will have to take it from here...

Posted by Jyqm on 2008-06-11 19:29:07