)
if you or any reader finds mistakes or wants to suggest improvements or
enhancements, I would be glad to correspond with you!
-- Steve
Bergen (e-mail: )
p.s. No answers yet are posted to these treats. It is important to
think about these treats for a while and to share ideas with friends,
teachers and other students. If I posted answers, it would deprive you
the of the tremendous joy of pondering these problems. Once you have
thought about it for a while and shared thoughts with others, I would be
glad to "check your answer" and respond to you via ;
happy thinking .... Steve
>Subject: Re: The next letter is... >Date: Wed, 22 Feb 2006 20:12:17 -0500 > >"Kimberly Martin" on Wednesday, February 22, 2006 >at 12:35 PM -0500 wrote: > >N. My reasoning is that the letters that contain any curves > >(non-straight > >lines) are omitted. > >I enjoyed your Web site! > >Kim > >Massachusetts I'm an accountant going back to school for teaching and I tutor on a part time basis. Would you mind if I use that trick for my education class? Not a problem! Keep up the good site! =o)
Mr. Bergen, I would very much like to figure out the answer to the finger snapping problem I just can't remember how to do it.Ê I've done a problem very similar to this one but i can't remember the formula that is used.Ê Do you think youÊcould help me out? Thanks, Tyler Ksolution as JPEG graphic
solution as EXCEL spreadsheet
Pete Peters -- melisma90 AT hotmail.com -- 1/11/08 wrote: Forgive me if I am writing to where I shouldn't be writing but I came across your program on math tricks/problems etc and before I die [I'm 72] I would like to find how a trick my father taught me, many years ago, actually works. I've searched since I was about 20 for the answer. The trick was this :- A farmers house had a window in each of the 4 walls. Out of each window he could see 7 men working in the fields and didn't want to see any more than this. One day a man came looking for work but was refused as the farmer wouldn't have 8 men in one of the fields. The man said if I can arrange it so you will never see more than 7 men will you give me a job? The farmer gave him a job and indeed he never saw more than 7 in each field. This happened again & again with more men and even though about 10 or more men applied for jobs the farmer never could see more than 7 men in each field. My dad taught me this and I managed to do it a few times but as the years flew by the procedure flew by as well. If you have the answer to this I would be very grateful to receive it. Thanks, Pete Peters
Undisclosed-Recipient AT cox.net on June 1, 2008 at 1:08 PM -0400 wrote:
Steve: The newspaper presented an interesting math problem this morning. It said a man from Dallas had paid $6 for his $3 parking ticket in Wisconsin. Twenty-one years late. But the article also said: A notice on the ticket indicated that failure to pay within 120 hours would result in doubling of the $3 forfeiture. I thought it would be fun to figure out what he really owed, if you get my drift. It's similar to that old double a grain of rice over the 64 squares of a chessboard problem.Ê As I have it figured, you need to double $3 1,533 times. I found your finger snap problem and thought I'd let Excel do the hard work the same way (instead of me pushing x2 on a calculator that many times. The number gets so big that Excel refuses to play after a while. How else do I find the answer, in the computer age? Steve P.S. Excel quit at the number 1.3483E+308 What is this number? 1.3483 X 2.71828183 followed by 308 zeros? Steve: I'm a lawyer in Phoenix, Arizona. I don't have much occasion for math in my line of work. But my calculus professor in college had to throw out my test scores because they skewed his curve so radically. (I leave to you to speculate on which end of the curve.) (When I pull out those tests now, I have no clue what I'm looking at.) I also used to substitute teach fourth graders in the Washington School District here in Phoenix. And I'm thinking of teaching 4th graders full-time as an "encore career" in another 10 years or so. I enjoyed your webpage. Steve
hello Steve ... I met a math teacher in California this summer and shared your problem with him ... here is his response hope this helps ... Mathematica is a high powered software program .... my friend confirmed that there was no easy trick in Excel ... Steve
Hi Steve, OK, so there are 1,533 120-hour periods in 21 years. The value we want, then, is 3 x 2^1533. When I tried it in Excel, I got the same result as your email correspondent. Excel wouldn't compute past 3 x 2^1022, which is 1.2483 x 10^308. So I turned to Mathematica, which can compute the value of 3 x 2^1533 with ease. The answer is: 903867160095387220717543727260617792342034967979633356759878139649471521846926200250906884040254768623793287355333001795448406367048109371863604870459040494295705002268109459289043279219130562378817078676520432521599004696714224666048020170787315486874180865503362754111052508230606535654422811487919701388888363415958096978645337004336034418780217345444087872643084606303742486693068148926827515693347689842622314212014739129697191246650462370071376785127243776. In scientific notation, this is 9.039 x 10^461.
This is a neat problem that comes from Ask Marilyn in Parade Magazine January 16th 2005 and was submitted by Michael Storey from Kingston WA: "At 60 mph, it takes 60 seconds to travel a mile. At 120 mph, it takes 30 seconds. At what speed would it take 45 seconds?" I will re-phrase the question in terms of race car drivers Alice, Barbara and Carol: --> Race car driver Alice drives at 60 mph and takes 60 seconds to travel one mile. --> Race car driver Barbara is much faster and drives at 120 mph; it takes Barara 30 seconds to travel one mile. --> Race car drive Carol has a broken speedometer but travels one mile in exactly 45 seconds. What was her speed? This neat sequence of letters comes from a colleague in California (Kyle Krupnick) who like me is fascinated with puzzles and whose youngest daughter used this Web page to mastered most of these amazing math tricks ... he writes that "I have never seen her so excited" and poses the letter sequence of A E F H I K L M and challenges readers to guess the next letter!
CHOP THE NUMBER IN HALF. IF THE
RESULT IS EVEN, JUST ATTACH A FINAL
ZERO. IF THE RESULT IS ODD, THEN FORGET
ABOUT THE REMAINDER AND JUST ATTACH A
FINAL FIVE. THIS TRICK WORKS BECAUSE
MULTIPLYING BY 5 GETS THE SAME RESULT
AS MULTIPLYING BY 1/2 x 10.
EXAMPLE: 5 x 468 = 2340
ANOTHER EXAMPLE: 5 x 467 = 2335
ALTHOUGH MOST PEOPLE JUST MEMORIZE THE
EASY SQUARES, AN INTERESTING PATTERN IS
THAT THEY INCREASE BY JUMPS THAT MATCH
THE ODD NUMBERS. CONSIDER ...
1,4,9,16,25,36,49,64,81,100 ...
THE GAPS BETWEEN THEM ARE 3,5,7,9,11 !
HERE IS A GREAT TRICK FOR SQUARING A
TWO DIGIT NUMBER THAT ENDS IN 5: TAKE
THE FIRST DIGIT AND MULTIPLY IT BY THE
NUMBER THAT FOLLOWS IT IN THE 'NUMBER
ALPHABET'. THEN ATTACH A 25 AND YOU ARE
DONE. FOR EXAMPLE, TRY 75 X 75. SINCE
7 X 8 = 56, THE ANSWER WILL BE 5625 !
THE TOUGHER SQUARES CONTINUE THE SAME
PATTERN OF ODD NUMBER JUMPS THAT THE
EASY SQUARES STARTED: 121,144,169,196,
225,289,324,361,400,441,484,529,576,625
NOTICE THE JUMPS OF 23,25,27, ETC.
ALSO, NOTICE THAT 12^2 = 11^2 +11+12.
THIS RECURSIVE PATTERN ALWAYS EXISTS!
WHEN YOU MULTIPLY 11 BY A 2 DIGIT
NUMBER, AND THE SUM OF THE 2 DIGITS IS
BIGGER THAN 9, THEN YOU MUST MAKE THE
SUM FLY DOWN ON TOP OF THE PATTERN,
"WITH 1 # LANDING IN THE HOLE AND 1 # ON"
TOP OF THE LEFT NUMBER, BUMPING IT BY
1, WHICH IS REALLY A CARRY. CONSIDER
48 X 11 ... WE HAVE 12 LANDING ON 4-8
"... THE 2 FLIES INTO THE HOLE ... 528 !
THIS TRICK JUST EXTENDS THE 11 TRICK,
EXCEPT YOU STUTTER ONCE WITH THE
NUMBER IN THE HOLE. FOR EXAMPLE, SINCE
11 X 35 = 385, THEN WE WILL HAVE
111 X 35 = 3885, WHERE THE 8 JUST GOT
REPEATED AN EXTRA TIME. AND WHAT DO"
YOU THINK THE TRICK FOR 1111 WILL BE ?
VOILA ... 1111 X 63 = 69993 !
TO CHECK YOUR ANSWER, WHEN YOU MULTIPLY
BY 3, THE DIGITS OF THE ANSWER WILL
ALWAYS ADD UP TO BE A MULTIPLE OF 3.
FOR EXAMPLE, 3 X 9 = 27 AND 2 + 7 = 9.
OR TRY 3 X 56. THE ANSWER IS 168, SO
ADD 1 + 6 + 8 TO GET 15, WHICH IS A"
MULTIPLE OF 3. AND SO IT CHECKS!
ONE WAY TO MULTIPLY BY 4 IS TO DOUBLE
THE NUMBER TWICE--THIS WORKS BECAUSE 4
EQUALS 2 X 2 !"
IF YOU WANT, YOU CAN DOUBLE THE NUMBER
THREE TIMES, SINCE 8 = 2 X 2 X 2 !
FOR EXAMPLE, CONSIDER 8 X 7. TAKE THE
7 AND DOUBLE IT. YOU GET 14. DOUBLE 14
TO GET 28. THEN DOUBLE IT ONE LAST TIME
TO GET 56. YOU'RE DONE -- 7 X 8 = 56.
8,16,24,32,40,48,56,64,72,80 ...
WHEN MULTIPLYING 9 BY ANY NUMBER > 1
& < 10, YOU WILL GET A 2 DIGIT ANSWER."
DIGIT ONE WILL BE 1 LESS THAN THE
NUMBER TO BE MULTIPLIED AND YOU CAN GET
DIGIT TWO BY SUBTRACTING DIGIT ONE FROM
9. CONSIDER 9 X 8. 1 LESS THAN 8 IS 7."
7 FROM 9 IS 2, SO THE ANSWER IS 72."
9,18,27,36,45,54,63,72,81,90 ..."
TREAT THE NUMBER IN THE TEENS AS A SUM
OF A SINGLE DIGIT AND A MULTIPLE OF 10.
THEN GET 2 ANSWERS AND ADD ...
FOR EXAMPLE: 7 X 16 = 7 X (10 + 6) ="
70 + 42 = 112 !
WHEN YOU MULTIPLY 11 BY A 2 DIGIT
NUMBER, PUSH THE NUMBER APART, YIELDING
A 3 DIGIT NUMBER WITH A HOLE IN THE
MIDDLE. THEN, IN THE MIDDLE, PUT SOME
NUMBER, THAT IS SUM NUMBER, THAT IS THE
SUM OF THE TWO OUTSIDE NUMBERS GOES IN
THE MIDDLE. FOR EXAMPLE, 11 X 34 = 3?4
WHICH GIVES US 374 !
STEP 1: ADD EITHER NUMBER TO THE ONE'S
PLACE OF THE OTHER NUMBER.
STEP 2: MULTIPLY THE STEP 1 ANS. BY 10.
STEP 3: MULTIPLY THE ONE'S PLACES OF
THE ORIGINAL TWO NUMBERS.
STEP 4: ADD STEP 2 TO STEP 3. VOILA !
FOR EXAMPLE: 13 X 18 ... 21 ... 210
3x8 = 24
now add 210 + 24 to get 234
On Saturday night, 1/10/2004 when the New England Patriots beat the Tennessee Titans,
a frozen football with ice was found weighing 6 pounds plus half its weight. How much did it weigh? (suggested by Jon Latson RI)
This is a classic problem (mathmatical hall of fame) from the book series TC Mits and TC Wits.
Tie an imaginary belt (perhaps with rope) around the equator of the earth. Let us assume it is 25,000 miles. Make this belt so tight so that you cannot fit even a pencil or a pin under it, let alone a finger. Now add 10 feet of rope to this belt, so that it is 25,000 miles plus 10 feet. Pretend that you can distribute the rope evenly around the earth so that it is uniformly "loose" around the entire earth. How loose will the new belt be? Would a dog be able to walk under it? Could I stick my fist under it? What about a finger or a pen or pin?
Snap your fingers. Wait 1 second. Snap again. Wait 2 seconds. Snap again. Wait 4 seconds. Snap again. Each time, your "wait" will be double the previous time. Do this for one year. How many times will you have snapped your finger?
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