What's the deal with those "add a number, multiply by 50 and get your age" emails?

Factual Questions
1

Every once in a while my mom forwards me an email like this:

So, this works for my 76 year old ma and 37 year old me. I’ve seen other emails just like it.

What is the trick? (Or the math that allows it to be true)

Is there anyone this wouldn’t work for?

Why wouldn’t this work in another year?

2

You can figure it out with algebra:

  1. First of all, pick the number of times a week
    that you would like to have chocolate.
    (more than once but less than 10)

We’ll call this x.

  1. Multiply this number by 2 (Just to be bold)

2x

  1. Add 5. (for Sunday)

2x+5

  1. Multiply it by 50.
    I’ll wait while you get the calculator…

100x+250

  1. If you have already had your birthday this year
    add 1754…If you haven’t, add 1753 …

100x + 2004, or 100x +2003

  1. Now subtract the four digit year
    that you were born (Call this year y).

100x + (2004 - y), or 100x + (2003 - y)

Do you see how it works now?

3

shrug It’s not all that amazing.

I mean, think about it - if you take the year 2004 and subtract the year you were born, you get your age, as long as you’ve had your birthday already. If you add 200 years to 2004, and end up with 2204, and subtract the year you were born, you end up with 200 + your age.

The only trixy bits here is that instead of just adding 200, they start with a number you pick and do some gobledegook math designed more or less to confuse the issue (steps 1 through 4). Step 5 is a number that simply negates all the multiplication added in the first steps, and adds enough to come up with 2004 + (# of times you eat chocolate * 100). Step 5 also takes care of the birthday issue by subtracting 1 if you haven’t had your birthday yet (ie, if you were born on Jan 1, 1970 (which is coincidentally MY birthday :D), 2004-1970 correctly states your age. If you were born on December 31, 1970, you have to subtract 1 to the result because you haven’t had your birthday yet this year).

So really, all they’re doing is adding in some bogus number to 2004, then subtracting them out and you’re supposed to be amazed.

4

There are lots of these arithmetic diversions circulating around the Net, or ones like it. If you remember your algebra, you can track the steps and see how the “program” is reaching its results.

In this particular case, the first step is essentially limiting you to a digit from 2 to 9. (I don’t know why the author excludes 1. It wouldn’t break anything.) Call this number N.

The next three steps result in 50 x (2N + 5), which is also 100N + 250.

The next step results in either 100N + 2004, if you’ve had your birthday this year, or 100N + 2003 if you haven’t. Note that your current age (A) is either 2004 minus your year of birth (Y) if you’ve had your birthday by now, but is one less if you haven’t yet. So A = 2004 – Y in the first case, and A = 2003 – Y in the second.

Therefore, when we get to step #6, we’re computing either 100N + 2004 – Y or 100N + 2003 – Y, which is 100N + A, regardless of which of the two cases is true.

So finally we have a number of the form 100N + A, where N is a single digit, and A is your age. As long as your age fits into two digits (true for most people receiving this chain email, I would imagine), then the stated “miracle” will indeed be realized.

And yes, this little procedure only works for 2004. Other years would require different constants in step 5. (In software engineering, that’s called “using a hard-coded constant”, and is considered bad form.)

5

Well, I’m no math whiz but… the add 1754 “if you had your birthday this year” - that’s the tip-off. Very specific, and depends on the date you were born. That’s where I started - knew there had to be a link between 1754 and 2004

let x = the number you chose

Multiplying it by 2, adding 5, and multiplying by 50 is the same as:
(2x + 5) * 50, which works out to

100x + 250

now add 1754 “if you had your birthday”

100x + 250 + 1754 = …ready??

100x + 2004

If you subtract the year you were born from that, you get the number of times you’d like chocolate in the 100s position (because you multiply it by 100 per the formula), and your age filling in the 10s and 1s positions. Obviously, 2004 minus your birth year results in a 2 digit number - your age. Unless…your 100 or older.

Try it with a woman fortunate enough to have lived to 102. It doesn’t work, because part of her age fills in the 100s position, and that’s ‘supposed’ to be empty and available for the # of times chocolate * 100 to occupy. Let’s say this 102 yo (born in January) likes chocolate twice a week:

22=4
4+5=9
950=450
450+1754= 2204
2204 - 1902 = 302…which would mean she likes chocolate three times a week, and she’s two years old. Clearly this is incorrect. All 2 year-olds like chocolate way more than twice a week.

See what happened? Her age of 102 took up the 100s position, and screwed up the trick. However…add her age digit from the 100s position (1) to the number of times she likes chocolate (2), and you get the digit in the 100s position from the ‘trick’: 3.

Next year, the ‘magic number’ will be 1755 ‘if you’ve had your birthday already’…and 100 year-olds will still screw it up.

Jake

6

I see now. I knew it was a trick, but I couldn’t figure out the twist. The numbers seemed so random (especially the 1754). I’m not of a mathematical mind, so I couldn’t make the connection.

Thanks Dopers!

7

note to self:

  1. preview * all the way down*

  2. Work stuff like this out * proir to* hitting “reply”; don’t work it out * while * replying.