Coke has been running is My Coke Rewards program for more than a year now, offering soda drinkers the chance to earn "rewards" for just being loyal soda drinkers. Since I'm on a 2-3 Diet Coke-a-day habit, I've been saving my bottle caps and earning reward points (usually 3 points per bottle cap).
To track points, you go to a Coke Web site and type in the 12- or 15-digit code found on the bottle cap, and the system awards you the points. If you have enough points, you can then redeem them for various prizes or other rewards. If you mistype the code, the software politely tells you that the code isn't valid, and asks you to double-check the code.
Earlier today I was typing in the code, and the system kept telling me the code wasn't valid. After the third time typing it in, I realized the cap was upside down. Yet every number and letter in this particular code could be read upside down or right-side up. The incorrect code was "HW6N66WW00W6" – when I turned it the correct way it was "9M00MM99N9MH".
My computer technology brain started ticking. First, shouldn't the program that assigns the codes try to include at least one letter or number that can't be misinterpreted when upside down? Since you already have a program that generates a random code and then has to track it in a Web database (to confirm real codes vs. fake ones), it shouldn't have been too much of a problem to guarantee that each code has a non-upside-down number in it.
Then my math brain started ticking. What are the chances of getting a code that could be read both ways? With a choice of 26 letters, 10 numbers (zero through 9) and a 12-digit code (I'll ignore the 15-digit codes for a second), that gives the possibility of 4,738,381,338,321,616,896 different codes (36x36x36, etc., for 12 digits). For you math majors, that's more than 4.7 quintillion possibilities.
So the odds of getting that exact code are one in 4.7 quintillion, but the odds are lower that I could get another cap code that could be read upside down correctly. Considering that the letters H, I, M (confused as W), N, O, S, X and Z, as well as the numbers 0, 6 (read as 9) and 8 could be read upside down (I'm also assuming the number 1 has the base on it and isn't just a straight line), that's 13 different characters that could be combined into a 12-digit upside-down code. Following this logic, 13 to the 12th power would give you 23,298,085,122,481 or about 23 trillion upside-down codes.
At this point my head started to hurt with all of the math, so I'll let the readers take this on further (and correct my math or logic). Not knowing the number of valid codes that Coke has distributed (let's assume they picked 1 billion valid codes), what are the chances that there's another upside-down code available?
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You lost me at 4,738,381,338,321,616,896
OMG my head is spinning. All I can add is that the chances are very small and leave it at that. I'm super-impressed with the math skills!
Upon further thinking...
We could be getting closer on this, or further away as my math logic gets worse. Over the weekend I thought, "Calculate the percentage of upside-down numbers vs. total combination of codes, then apply that percentage rate to the 1 billion code assumption to estimate the total number of potential valid upside-down codes." This assumes, of course, that the percentages stay the same between the total number available and the lower number of codes that Coke produces for this promotion.
With that in mind, I figured that the percentage of upside-down codes compared to all codes is .00049% (pretty low). However, if Coke picks 1 billion valid codes, and the percentage stays the same, that leaves us with about 490,000 potential valid upside-down codes out there for me to find. My percentage calculation could be off, though, it could be .0000049%, which would leave only 4,900 potential valid codes. But I think I did the math right on figuring out the percentage (divide total upside-down codes by the total of all codes, then multiply by 100).
Anyone still with me?
Does somebody need a girlfriend?
Does soembody need a girlfriend, like, A LOT? After seeing all the energy that's been put into this silly topic, I'd say someone should be answering in the affirmative.
:-)
Proving once again...
... that the 'wisdom' of the crowd is much better when you allow anonymous commenting. By the way, my wife will be happy to hear that you would like me to get a girlfriend.
I LOLed Great Math btw. Must
I LOLed
Great Math btw. Must have been bored :D
well, it was summer time...
Things tend to get slow during the summer, as you all know... :D
vaild codes
I wonder what the odds are that an upside-down code might be valid. But, I don't even want to think about whether that's a number that can be calculated from your other numbers or not. One would have to know what algorithm validates a given code....
random code generator?
My best guess is that it's just a random code generator, with another program / database that has the list of valid codes.
Ha
Being a Diet Coke Fan (at least three in the morning to get me going) and a Rewards participant, thought this was pretty good...although the math hurt. Us communication/marketing folks don't like math that much.
think about this
ok so theres a generator that just makes random codes. Ever used a generator? well heres how it works it generates millions of encrypted codes that are saved in a database where they are stored until used, then it is crossed off from the list and each time 1 code is used 2 more are generated and while this is generating the computer or personel is recording this to be printed on caps. pretty much what they are doing is producing more and more each time you enter a code because this assures them that they have customers trying to earn rewards so maybe the math of an upside down code is a lot but relly why this about that when perhaps if you are a good hacker get the list of encryptions and uncrypt them maybe using cane or another program of similar functions.Oh and this is writen by a 15 year old and i didnt care about the spelling so I dont care if its wrong it got the point across.