Index | Comments and Contributions | previous:12. pranks and accidents
mathematics
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From: Candie 1) Pick a number between 1 and 9 2) Subtract 5 3) Multiply by 3 4) Square the number 5) Add the digits of that number together, for example, if you number is 83, you would add 8 and 3 and get 11. 6) If the resulting number is less than 5, add five, otherwise subtract 4 7) Multiply by 2 8) Subtract 6 9) Assign a letter to your number. A=1, B=2, C=3, D=4, E=5, etc 10) Pick a country that begins with your letter 11) Pick an animal that begins with the second letter from your country 12) think of the color of that animal.... If you did this right and didn't pick something off the wall for the animal or country, you should come up with... A grey elephant from Denmark. (The trick is in step5. 3) and 4) caused the number to be a multiple of 9 and the sum of the numbers of a multiple of 9 is again a multiple of 9, in this case 0 or 9. Step 6 equals these situations and if you do not think of the Dominician Republic you get Denmark for number 4. The elephant is the easiest animal with 'e'.) From: Alissa Mower Clough <teleny#NoSpam.server2.comm2net.com> The Order of the Elephant is the highest decoration in Denmark. It really is. Makes a nice comeback if someone springs this particular puzzle on you....
mathematics
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From: "Harold E. \"Mac\" McKinney" <mcvistas#NoSpam.abaco.coastalnet.com>
Tell someone to write down a 3 digit number (example: 746) Tell them that
you are each going to write down 2 more 3 digit numbers and add them, but
before you do, you are going to write down the answer on a piece of paper
and fold it up. You obtain the answer by subtracting 2 from the last digit
of the first number and placing a 2 before the first digit--thus 746
becomes 2744 for the answer. Now ask the other person to put their two
digits down, either both at once or in succession with you. Either way,
they must preceed you. Now , whatever they put down, make each number,
when added to the number you put down add up to 999. Don't do this but
once with each person; they'll catch on otherwise.
Demo: (original number) 746 (Their first number) 325 (your first number)
674 (their second number) 841 (Your second number) 158
____ Total 2744
They unfold the paper and you're a hero!
mathematics
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From: dleqc#NoSpam.qcunix1.acc.qc.edu Here's another math trick involving "casting
out the nines":
Tell someone to do the following:
(1) Write down a three-digit number (where the digits are different), and
keep it hidden from you. (2) Reverse the digits and write that number
down. (3) Subtract the smaller number from the larger number. (4) Find
the same page in the phone book as the answer in (3) and remember
the first and last names of whoever is listed at the top of the first
column there. (5) Close the phone book. (5) Tell you just the *first*
letter of the last name.
You then open the phone book to the page containing that name and
announce the full name of the person.
Here's how it's done:
Whatever number the person selects in (1), the answer in (3) will
contain a 9 in the middle and the first and third numbers will add up to 9.
If, for example, the person writes down 623, this number reversed will
be 326. When 326 is subtracted from 623, the result is 297. Note that the
middle digit of this answer is 9 and that the sum of the first and last
digits is 9.
Whatever letter the person gives you as the beginning of the last name,
there will be only be *one* page number in the book (unless you live in an
extremely populous city!) where the names begin with that letter, have a 9
in the middle and the first and third digits add up to 9. Find that page
and read off the first name on it to the amazement of your victim.
mathematics
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Confuse people with the following riddle: Three friends go to sleep in a hotel. The man at the desk ask $30 for the room. (This is old...). After they pay $10 each and they went to their rooms, the manager comes in and tells the receptionist that that was the price for the expensive rooms. The cheap rooms the friends toke only cost $25 , so give them $5 back. The receptionist thinks it is difficult to divide $5 among three people, they would be happy to get something back and would not begrudge him some money for his trouble, gives the customers $1 each and keeps $2 for himself. So the friends pay 3*9 is $27 for the room and the receptionist gets $2, together $29. Where has the last $1 gone?
mathematics
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From: "DAREN M BAAK" <dbaak#NoSpam.prodigy.net>
Here is a nice way to introduce identities to a beginning algebra class...
Ask the class to chose any number, but to keep it a secret.
Add and subtract some numbers, eg. add 37 to the number, subract 86, then add 3.
Now subtract the result from the original secret number.
No matter the secret number, everyone finishes with the same number - in my example, 46.
As a trick to amuse the class, write the final number (in my example, 46) on the back of your hand in soap before class. After the class finishes with the manipulations, ask one of the students to crumple the paper and give it to you. Burn it, then rub the ash on the back of your hand and the number written in soap will become visible.
The explaination goes something like this. The secret number we will call n.
n + 37 - 86 + 3 = n - 46 subracting the result (n - 46) from the origninal secret number n, n - (n - 46) = 46 is an identity (the result is not dependent upon the number n).
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From: Nathan Curtis <jonathan.curtis#NoSpam.tufts.edu>
IS PRIME FACTORIZATION UNIQUE?
This one isn't one of those math tricks like the above, but is definitely more
of a "prank". During the summers, I teach mathematics at a summer program for
gifted youngsters, and year after year, my friends who teach Number Theory come
up with the most creative things to do with the material. They give famous
mathematicians alter egos, perform skits and songs like you wouldn't believe,
and basically do anything and everything to keep the students on their toes.
Sometimes their antics go a bit too far, and this is the story of one such antic.
In teaching the Fundamental Theorem of Arithmetic (i.e., every integer >1 has a
unique prime factorization), they spend some time convincing the students why
this fact isn't really as obvious as they have come to accept it -- who wants to
spend time proving a patently obvious statement? In particular, they focus on
the case of uniqueness -- why couldn't it be the case that some number can be
factored in two different ways? Traditionally, they give an example of a
"bi-factorization" in which they multiply two two-to-three-digit primes,
casually forget to carry one of the digits, and then note that the resulting
"product" is obviously divisible by some smaller prime like 3 or 11. This, of
course, relies on the students not immediately going to their calculators, and
none of them being quick enough to immediately spot the multiplication error. A
couple of years ago, a couple of the instructors (there are 5 or 6 folks who
teach Number Theory, and which 2 happen to co-instruct for any particular class
is difficult to predict in advance) decided to update this trick, as well as
much of their other material, for the 21st century. They developed a series of
Maple worksheets to illustrate many of the topics for the class, so the students
can see how some of the mathematical techniques are actually implemented
algorithmically. Early worksheets include testing for divisibility, testing for
primality, and prime factorization. It is the latter worksheets which concerns us.
In the morning, when they first talk about the universal existence of prime
factorizations, they roll out a worksheet to perform such a task. The program
might look something like this:
>program FactorList(n):
>[i:=2;
> while n<>1 repeat
> [if Remainder(n,i)=0 then
> [print(i);
> n:=Quotient(n;i)
> ]
> else i:=i+1
> ]
>]
It is simple and obvious enough -- start out by testing out 2 as a factor,
increment until a factor is found, divide and repeat. They would run the
worksheet, and it would run something like:
>FactorList(84)
2
2
3
7
>
Very well and good. Then in the afternoon, when talking about uniqueness, they
start off with a continuation of this worksheet, which says something like:
>{Most of you have probably gotten used to the idea that unique factorization holds
>for all numbers, and this is true, to a point. For smaller numbers, like:}
>
>PrettySmall:=(7^5)*(11^3)*(13^4)*(17^2)*19*(23^2)*(29^3)*31*(37^2)
1920913975247700797513001853
>
>{Unique factorization does indeed hold true:}
>
>FactorList(PrettySmall)
7
7
7
7
7
11
11
11
13
13
13
13
17
17
19
23
23
29
29
29
31
37
37
>
>{However, for larger numbers, like the size used in cryptography:}
>
>PrettyBig:=(11^33)*(17^26)*(29^19)*(31^14)*(41*11)*(47^8)
137930886415613597544460121580679226088322750664067060191669
636504511597226202112541884646283216388663617375284057146786
955752299746966906146186911
>
>{Unusual results can occur:}
>
>FactorList(PrettyBig)
At this point, there is a perfectedly timed pause of about 10 seconds, as the
computer grinds through the calculations. Suspends builds. Suddenly, it spits
out something like:
13
13
13
...
13
19
19
...
19
23
23
...
In other words, a COMPLETELY DIFFERENT set of prime numbers from what went in.
The class goes wild. Their whole world turns upside-down. All but one of them
are suddenly and utterly convinced that unique factorization is a myth, and the
one dissenter is on shaky grounds.
"But the original number couldn't possibly be divisible by 13," he says. "No
13's ever went into it. You can't multiply 11 by 17 and get a multiple of 13."
"No, but when you multiply by a lot of 11's and 17's, and throw in some of those
other numbers, it BECOMES divisible by 13!" his classmates respond.
The instructors were worried. They were certainly intending to shake the class
up, but they figured on the students being more skeptical. How to repair the
damage?
First thing, they called an emergency ten-minute break. When class resumed,
they decided to give everything away.
"Well...this is certainly an unusual result," one of them says. "And when you
get an unusual result, one of the first things you should do is check your code,
to make sure you haven't made any mistakes." So he scrolls up to the definition
of the FactorList program...
>PROGRAM FactorList(n):
>[IF n=(11^33)*(17^26)*(29^19)*(31^14)*(41*11)*(47^8) THEN
> n:=(13^33)*(19^26)*(23^20)*(37^13)*(43^9)*(53^8)
> ELSE
> [i:=2;
> WHILE n<>1 REPEAT
> [IF Remainder(n,i)=0 THEN
> [print(i);
> n:=Quotient(n;i)
> ]
> ELSE i:=i+1
> ]
> ]
>]
Hmm...there appears to be something there that wasn't there before. And what it
seems to be doing is switching the value of PrettyBig for another (also pretty
big) number, whose factorization happens to match that which the program spit
out previously. Almost as if it was put there on purpose...
"Huh," says the instructor. "I wonder how that got there. I'm not sure it
belongs."
"Go ahead and take it out," say the inadvertently brainwashed students. "We'll
still get the same results."
I know, I know -- they JUST gave the trick away, and the students are still
convinced it will work. This phenomenon is not unheard of -- psychics,
magicians, faith healing -- but even 10th graders smart enough to be taking
Number Theory are not immune to its effects.
So, of course, the teachers run it again, and you know what happens
>FactorList(PrettyBig)
11
11
11
...
11
17
17
...
17
29
...
>
That is to say, they get exactly what they SHOULD have gotten the first time.
Will this convince the students? Let's see.
"Oh, of course it will come up with that factorization. After all, they're BOTH
valid, so there's no telling which one we'll get."
The program is run a several more times, and from now on, it emits nothing but
11's and 17's and 29's...just as it ought to.
"Well, now that you took out that one line, it will always find the one with the
11's first. Since 11 is smaller than 13, it will hit 11 before 13, and go to
that factorization."
Well, why not multiply out the second factorization, and see if it matches.
Unfortunately, the instructors were almost too clever in this regard -- they
chose a pair of factorizations which matched for an awful lot of digits, and
which passed all the other rudimentary tests (checking the last digit, casting
out 9's, etc. The factorizations I gave above are not quite right, as they
don't match up nearly as well as theirs did). If you multiplied them out on
most calculators, they would be equal as far as their precision could handle.
Fortunately, Maple's "infinite precision" showed that the two numbers were not
the same, and order was eventually restored, though it cost the teachers over an
hour of classtime and a week of trust. These teachers love crying wolf so much
that their main concern for the repercussions was not that they might not be
taken seriously when giving them straight facts, but but that they wouldn't get
the students to fall for any other jokes later on.
The moral of the story: You can get anyone to trust anything if you have a
"computer program" backing you up. For most people, GIGO means "Garbage In,
Gospel Out." The instructors were able to repeat the trick the next year, but
they learned from their experience and installed safeguards to prevent the
students from being too taken in. At the beginning of the false factoring
program, they added a comment:
>{Hey, guys, check out this factoring program I wrote. I think you'll really
enjoy it.
> -- Jeff}
Here, Jeff is a former instructor who is well established (within the classroom
universe) to specialize in faulty math -- his "proof" of the Pythagorean Theorem
(as relayed by one of the current instructors) is that in a 3-4-5 right
triangle, 3^2+4^2=5^2. Consequently, his named attached to anything is cause
for suspect. As a result, this time they had to actually work a little bit to
keep the students suitably gullible -- one of the students had a calculator with
sufficient precision, and was able to see right off that the two factortizations
didn't multiply to the same product. They replied, "Well, what are you going to
trust: your hand-held TI calculator, or this Maple Worksheet?" He swallowed
their line.
Corollary to the above moral: the fancier the computer, the more credulous
people will be.
Exercise: devise a presentation, using an appropriately powerful computing
system, (Cray supercomputer, Beowulf cluster, infinitely many monkeys with
TI-83s) which will subvert all major religions and belief systems. Extra credit
for toppling world superpowers.
next:12.2 burning metals | Index | Comments and Contributions
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