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.
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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.
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