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## bruce hurley .com

 my life is nothing like this

your age by chocolate--solution

I've had a few people forward this mathematical riddle to me for explanation, so here it is.

The effect of this riddle is to calculate your age by how many times a week you would like to have chocolate.

Your Age By Chocolate: The Effect
(as spread around the Web)

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

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

• Add 5 (for Sunday).

• Multiply it by 50.

• If you have already had your birthday this year add 1754....If you haven't, add 1753.

• Now subtract the four digit year that you were born.

You should have a three-digit number. The first digit of this was your original number (i.e., how many times you want to have chocolate each week). The next two numbers are:
YOUR AGE!

THIS IS THE ONLY YEAR (2004) IT WILL EVER WORK, SO SPREAD IT AROUND WHILE IT LASTS.

The Explanation You Really
Don't Want To Read

If you think mathematical riddles like this are amazing and magical, it's probably best that you don't read this explanation (solution). Ask any magician: everybody says they want to know how a trick is done, but they're almost always disappointed when they find out. If you really want to know how it's done, it will be a lot more satisfying if you figure it out for yourself.

Age By Chocolate Explained

All riddles have a goal. The goal of this riddle is to create a very complicated way of doing a very simple thing. This is a common form of parlor trick (click here for a much simpler example), where you do several math steps and then several more that serve only to erase the first steps. The effect is that a complex mathematical calculation seems to magically create the answer, when actually it is a very simple calculation designed to appear complex.

A couple of the numbers are color-coded so you can track them through the calculations.

 For this example, let's use 4 times per week as your preferred chocolate consumption. We'll refer to this as your chocolate number. When you double any number, it automatically makes it even ( 4 x 2 = 8 ). When you add 5 to any even number, it automatically makes it odd ( 8 + 5 = 13 ), so by step three, everyone's number is odd. When you multiply any odd number by 50 the product will always end in 50 and the digit(s) before 50 will always be your chocolate number plus 2 ( 13 x 50 = 650 ). The 6 before the 50 is our chocolate number (which is 4) plus 2. The number 1754 is simply 2004 minus 250. The reason we subtract 250 from the current year is that this will always be the number necessary to erase most of the extra steps we performed in steps #2 through #4. The 2 in the hundreds position of 250 represents the extra 2 (see step #4 above) and the 50 eliminates the extraneous 50 we wound up with from the math in step #4. So far, all this math does is obfuscate the current year (2004), so that the calculation appears magical. You could just as easily have subtracted the 250 from your previous number (650-250 = 400) and added that to 2004 (instead of 1754), but that would have made it more obvious how this problem is related to the current year. Either way, it's the same answer: 550 + 1754 = 2,404 OR 400 + 2004 = 2,404. No matter what number you pick originally, this large number will always be 2004 (the current year) plus a multiple of 100 determined by your chocolate number (3 = 300, 4 = 400, 5 = 500). If your chocolate number is 7, then this number will be 2,704. Got it? When you subtract your year of birth, all you are doing is creating a number that is: Your age + (your chocolate number x 100). The only thing all this math accomplishes is to create an extremely complicated way to multiply your chocolate number by 100 and add it to your age. For instance, if a 40-year old's chocolate number is 5, then 5 x 100 = 500 + 40 = 540. If a 22-year-old's chocolate number is 7, then 7 x 100 = 700 +22 = 722. All the other math is erased in step #5 when you add 1754 instead of 2004.

The riddle as originally posed says to pick a number greater than 1, but less than 10. This is unnecessary because numbers of any size will always work, including 1, 10, and 12,983.

The riddle also says that 2004 is the only year this will work. That's true, but all you have to do is change the 1754 to 1755 and it works just as well for 2005. For 2006? You guessed it: 1756.

I told you you would have been better off thinking it was magic.

This riddle is actually quite boring except that some marketing genius decided to sweeten it up by calling it Age By Chocolate. By borrowing a universal cultural icon, a dry riddle is magically transformed into something fun.

Hmm. . . maybe there really is some magic here after all.

A Simple Parlor Trick

Here is a simple version of a mathematical trick, which you can use to amaze your friends and confound your enemies (presuming your friends and enemies are simple-minded):

 Ask someone to silently think of any two-digit number (or, if you don't know how old they are, have them think of their age). Tell them to silently add three to this number. Tell them to silently add another five to that number. Tell them to silently subtract one from that number. Then, tell them to silently subtract their original two-digit number from the final number. When they have that calculated, announce that they are left with 7. If they say that you are wrong, it is because they have done their math incorrectly. Make sure you go slowly. Remember, not everyone can be the genius that you are. This trick works because when our brains are busy performing calculations, we often miss the most obvious things. In this case, the obvious thing is that we have our victim add 7 to a number and then subtract their number. Obviously, you will always be left with 7.
 A great value in boxed chocolates

 © 2002 bruce hurley