I’m sure a question like this will sound extremely familiar to a lot of people who have been around the block a time or two.

If you were offered $1 million dollars or a penny doubled every day for a month (30 days), which would you choose?

The $1 million might sound like the best deal, but it’s not.

On day 1 you’d have a penny. On day 2 you’d have two pennies. Day 3 would be a whopping four cents. And it turns out that by day ten you’d have $5.12.

After that, however, things quickly begin to change.

Day 15 would be $163.84.

Day 20 would be $5,242.88.

On Day 28 something extremely interesting happens. You’d have $1,342,177.28, which is $340 thousand more than $1 million dollars.

On Day 30 you’d finally be done and you’d have over $5 million dollars. $5,368,709.12 to be exact. If you chose the sneaky penny doubling deal you’d end up approx. 5 times as happy. 🙂

Now all you have to do is sit around and wait for someone to offer you that deal.

I think a lot of us have probably heard some variation of this sort of thing before. The point is not subtle: Things that grow exponentially can get big very quickly.

I recently won a blog award and that got me thinking about this sort of thing. You see, the blog award has a rule that as a recipient of the award, you are asked to pass the award along to seven more bloggers.

See where I’m going yet? This is the exact same math problem, only instead of doubling per day it grows by seven times per interval.

Some assumptions we’ll make: The award will be passed on weekly to seven people. The following week each recipient will then pass the award on to seven more people. And so on and so on and so on. To keep things simple we’ll also make a rule that no one can receive the award more than once.

Week One starts with you and your award. Let’s assume you’re the first. Perhaps you invented the award and this silly little “chain letter” ruling in the first place! 🙂

Week Two you give the award to seven awesome peeps you know.

Week Three those seven people pass along the award to seven more people. That is 7 x 7 which means 49 people now have the award.

On Week Four those 49 people each give out 7 more awards. That is 49 x 7 or 343 people.

By Week Nine it would be about 9 million blogs.

Week 11 would be about 282 million blogs. It is interesting to note that as of Feb. 2010 WordPress estimated there were about 22 million blogs using WordPress software. That includes those hosted on WordPress.com and stand-alone software installations on other web servers.

Week 12 would be about 2 billion blogs. Week 13 approaches 14 billion blogs, which almost twice the people on planet earth. Week 14 is about 97 billion blogs. By Week 16 there would be about 5 trillion blogs to receive the award.

Going any further is just too darn silly, but I can tell you that by Week 30 the exact number of blog award winners under this scenario would be:

22,539,340,290,692,300,000,000,000

That’s a number so big I don’t even know how to describe it. My best guess would be 22,539 trillion trillion. Another way might be to say 22.5 septillion blogs. (A septillion is a 1 followed by 24 zeros.) For comparison it is estimated that the Death Star would have cost about $15.6 septillion. That’s about 1.4 trillion times the U.S. national debt. Meh.

I can say this much, though, with 100 percent certainty. Some people have clearly not been fulfilling their obligations to forward these “pass it on” type awards like they are supposed to! 🙂