McClane Distributing Plan

1456 Athena Drive

Athens, GA 30680


Dear Mr. Walter,

Our class was assigned to find a numbering scheme that would yield about 10 million slots in your center. This would be a great benefit for you if McClane ever decides to expand its capacity.

Right now McClane has 4,225,000 possible slots. This number is determined by multiplying the number of possibilities for each character in your current numbering scheme. Right now you have 7 characters in your scheme. The first two are letters representing the aisle, so this is 26*26 (26 letters in the alphabet). The next three numbers identify the bay area and are 0-9, so this is 10*10*10. But you use only every fourth number so it is really (10*10*10)/4. The next two numbers are shelves and slots per shelf. Each is 5. So if you multiply all of these possibilities you have 26*26*[(10*10*10)/4]*5*5= 4,225,000 possible combinations.

I have devised a way for you to have exactly 10,000,000, that's right 10 MILLION, possible combinations for slots.

It still uses 7 characters that will not change. But instead of using 26 letters use 25, throw away the Z. So you have 25 possibilities for the first and 25 for the second. That is 25*25. For the next three numbers instead of using every fourth use every one. That is 10 possibilities for the first, ten for the second, ten for the third, 10*10*10. Now you have 25*25*10*10*10. Right now you have 5 shelves for the each bay location, make it 4. You also have 5 slots for each shelve, also make it 4. So now you have 25*25*10*10*10*4*4. This is equal to exactly 10 million possibilities. This will increase your capacity to 10 million slots. Thanks and I hope this will be a help to you, have a good day.


Matthew Moon



The Department of Mathematics Education
University of Georgia