Memory Matching Expectations
Given an even number of squares (N) that are filled with paired objects (O), where O is N/2, and then covered so we can't see the objects, then how many blind (random) tries (consisting of two choices of different squares) are expected in order to match all the objects. The objects are matched by choosing two different squares at random (a try) and if the objects in these two squares match then they remain uncovered, but if they do not then both are covered again and their placement is forgotten. Certainly a person using their memory can match the paired objects faster, but we want to investigate the expected number of tries to complete the matching of all objects without memory.
Now Enter the number of squares:
Enter a guess for the number of expected tries:
Now click the button to see the correct answer:
Number of expected Tries =
to match all
The formula is Tries = 2 SUM (r=0 to r=n/2-1) n-2r-1