I got one of those fwd:fwd:fwd e-mails last week. Before I get to my obvious question, here’s the text:
First, I do understand that this has nothing to do with chocolate.
But, how does it work? (I can see that one’s age enters into the equation in step 6.) And why is 2006 the only year it will ever work? Couldn’t you change the number in step 5. to account for the current year?
No no no no no… it’s absolutely wrong.
You see, the first premise is wrong. “More than once but less than 10 times”? Hun, that won’t go!
You just need a little algebra to understand why this works. Let x be the number of times I want to [insert activity here], and y be my year of birth. The results after each step are:
[ol]
[li]Start with x[/li][li]Multiply by 2: 2x[/li][li]Add 5: 2x + 5[/li][li]Multiply by 50: 100x + 250[/li][li]Add 1756: 100x + 2006[/li][li]Subtract year of birth: 100x + (2006 - y)[/li][/ol]
(2006 - y) is, of course, my age; and if I’m not too old, then the first digit of the number I get will be x, the number of times I want to [insert activity here]. You’re absolutely correct in saying that the trick could be adjusted to work in future years; you just add 1 to the two numbers mentioned in step 5 for every year that goes by.
Assume that the number in step one is ‘n’. It’s pretty easy to see (with simple algebra) that the result will be
50(2n+5) + (1756 or 1755) - (birthyear)
100n + 250 + (1756 or 1755) - birthyear
100n + (2006 or 2005) - birthyear
Assuming (2005/6 - birthyear) is less than 100, n will always be the first digit, and (2005/6 - birthyear) will give your age. Tada! And it will work for any year, if you adjust the number in step 5. But it will never work for centenarians (without modification, that is).
Usually with these things, once you actually write down the algebra, you’ll see why it works. Let your original number be n. Then after step 2, you have 2*n.
After step 3, you have 2*n + 5
After step 4, you have 50*(2n + 5), which simplifies to 100n + 250.
After step 5 (assuming you’ve had your birthday), you have 100*n + 2006 (gee, does that number look familiar?).
Subtract out the year you were born, and you have 100*n + (2006 - birth year). But (2006 - birth year) is your age. So you have 100 times your original number, which makes that the first digit of the three-digit number, plus your age, the next two digits. Of course, if you haven’t had your birthday yet this year, then you need to be one year younger than this, so they tell you to add a lower number in step 5 to account for that.
And yes, as you surmise, you can change the numbers in step 5 to make this work for any year. And in fact this has been done, many times. The bit about it only working this year is just for this specific version with those specific numbers.
And people ask why we need to learn algebra in school.
Curse you, MikeS. :shaking fist:
And take that, Chronos. raises roof in triumph
You just proved that people really don’t as long as they subscribe to a good enough message board.
Ok, so when do I get my chocolate?
Y’know, that’s just what I was thinking. New motto: “The Straight Dope Message Boards: The world’s perfect resource for people who couldn’t be troubled to pay attention in school.”
I have to agree with you on this. In fact, I edited the original e-mail to make it shorter. The original had you pick the number, then scroll down to see that you couldn’t choose thirty- five, as I had done.
Thanks all. I had some of the algebra written down, but I didn’t carry it out far enough.
So, there’s really no chocolate?
…so we can figure out silly erzatz magic tricks that get forwarded to our work e-mail instead of actually working?
BTW, Sorry, I wish I could give everyone some real chocolate!