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How are you all celebrating PI day (3/14) today?
Dr. Pepper: i knew about that but i didn’t realize it was today til seeing your post. i’m not surprised it’s you bringing it up 😉
Dr. Pepper,
I found that hat riddle in an ad (I think for a consulting/ finance firm) in the Wall Street Journal this week.
Times up!
(from a puzzle magazine)
A kindergarten art class drew clock faces on paper plates.
They were standard analog clock faces like so:
.
12
11 1
10 2
9 3
8 4
7 5
6One of the boys got busy with his scissors and cut his clock face into four pieces.
As the teacher was taping his “clock” back together, she noticed that total of the numbers on each piece was identical.
1) What were the totals?
2) What numbers were on each of the four pieces?
Are you allowed to split 2-digit numbers? I think that’s the only way it makes sense?
~a~
Dr. – When on 3/14 was the “pi moment”?
anonymisss-
Nice catch!
That’s the key to solving the puzzle.
Now, provide the numbers…
Dr. Pepper-
Last year there was an article about a bunch of math enthusiasts who gathered in a bakery and at precisely “pi time” each had a slice of pie.
This year I didn’t see any such articles.
an open book-
I also forgot about it until today. When it comes out during the week we celebrate at work (pizza pies or something similar). Last year my mother-in-law made a custard pie and sent for Friday night dessert. But this year nothing.
We finally realized it after the seudah and decided to celebrate it though my wife gave strict orders to the kids not to tell any of their friends that we celebrated it.
that’s funny 🙂
Suppose you attach a distance measuring device, similar to an odometer, onto the front wheel of your bike. After a ride, the odometer reads exactly 1 mile. Had you attached an odometer to the rear wheel of the bike as well, would it show a distance traveled of exactly 1 mile, more than 1 mile, or less than 1 mile?
exactly 1 mile
squeak-
Assuming the following:
a) The wheels are the same diameter (some bikes, such as racing bikes, have a smaller front wheel to lower wind resistance).
b) The tires are equally inflated and have a similar load on them (also affects diameter).
c) The rider has not “skidded” either tire independent of the other.
d) An excessive number of turns has not been made (when turning a bike, car or other vehicle where the turning wheels are in front, the circumference of the turn is always greater for the front wheels)
e) The odometers are both made for the same diameter tires.
The front wheel will have will still have rolled slightly further, just because of the minute adjustments made by the bike rider in balancing and keeping to the course.
Well done, ICOT. The wheel that does the steering travels a greater distance because of minor (or major) wobbling.
that’s interesting
squeak-
Thank you.
In my (over)analysis of your question, I omitted the possibility of the biker doing wheelies, a la “Curious George Rides A Bike” 🙂
🙂
Times up! answer:
(“anonymisss” basically got it, but this is the full answer)
Each piece’s numbers total fifteen.
The 11 and 12 are split.
The four pieces look like this:
.
a)
1
1 1
10 2
b)
2
1
9 3
c)
8
7
d)
4
5
6Evening the Odds:
(from a puzzle magazine)
Toci, the game-obsessed, math-averse trivia fanatic noticed something about his favorite board games.
In all games that required a roll of two dice, the resulting numbers were not evenly distributed.
The odds of getting a:
1 were 0/36
2 were 1/36
3 were 2/36
4 were 3/36
5 were 4/36
6 were 5/36
7 were 6/36
8 were 5/36
9 were 4/36
10 were 3/36
11 were 2/36
12 were 1/36
Rather than accepting these inequitable odds, he designed a pair of dice whose sides would have an equal chance of producing all numbers from 1 thru 12 when thrown.
The redesign was accomplished incorporating the following facts:
1) Each die had six sides, with the odds of any one being landed on 1/6
2) Each side of each die can have from zero to twelve dots (no fractional dots)
How were the dice designed?
random guess-split odd/even numbers?
~a~
Evening the Odds – answer:
The six sides of die #1:
??????????????????????????????????????????????????????
? ??o ??o o??o o o??o o o??o o o o?
? o ?? o ?? o ?? o ??o o o??o o o?
? ?? o??o o??o o o??o o o??o o o o?
??????????????????????????????????????????????????????
The six sides of die #2:
??????????????????????????????????????????????????????
? ?? ?? ?? ?? ?? ?
? o ?? o ?? o ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
??????????????????????????????????????????????????????The odds of getting any number from 1 thru 12 are 3/36 (or 1/12)
A little Algebra-
Expand the following-
(x-a)*(x-b)*(x-c)*…*(x-z)
Dr. Pepper-
That’s a blast from the past!
My ninth-grade algebra teacher asked us that one many, many years ago (let’s just say sometime last century) and a certain wise-guy gave what turned out to be the correct answer, never suspecting he was actually correct.
Since:
a) I remember the original Q&A
b) I didn’t initially understand your question, so I googled it
…I can’t give the answer, but let me just drop a hint for others that not much math knowledge is needed, since this is a bit of a trick question.
x-x=0
multiply that by any amount of numbers and you are always left with zero.
and my knowledge of math is close to nothing
moish01-
You’re sharp as a tack!
That didn’t take long.
Dr. Pepper-
Hope you don’t mind I gave a hint for what was, after all, your question.
blunt tack you have there 😉
I typed the whole long equation (all 26 monomials) into my TI-89 during one particularly boring class and it took a considerable amount of time to get the correct answer of 0. It seems as if the calculator actually multiplied out until “w”.
Too bad it doesn’t have a right-to-left line interpreter. That would have cut the processing time by 91.66666%
oh don’t worry, squeak. i didn’t do the math. once ICOT said that there was a catch i was looking for it.
I was responding to Dr. P
oh i know. just mentioning.
I was actually kind of relieved that it took so long- it gave me something to look forward to.
You had to be sitting through that class to understand…
(It was also probably the first and only time that I was able to solve a problem faster than my good old TI-89.)
Which version of the 89…..? I used to have a 92, which was built like a laptop. Why don’t the numbers keep going up?
I have the original TI-89 that came out in late 1998- early 1999.
The original TI-92 which came out in the mid 90s was the first calculator that was capable of performing symbolic calculations (algebraic manipulations, symbolic differentiation/ integration, homogeneous first and second order differential equations…) as opposed to numeric approximations (like the TI-80 through TI-86). The TI-92 was not allowed to be used on many standardized exams (like the SATs) and many professors did not allow their usage in class since the QWERTY keyboard gave it more of a computer status than that of a calculator.
When the TI-89 came out TI released the TI-92 PLUS which looked like the TI-92 but had the same software as the TI-89.
TI skipped from TI-86 to TI-89 because at that time they claimed that the TI-89 would be the last calculator released in the TI-8X series since it has the capability of upgrading the software and downloading programs.
I lost touch with graphing calculators a few years ago (although I still have mine and use them from time to time). I think the version that I have has been discontinued for the TI-89 Titanium and TI added the TI-84 to the TI-8X family although I’m not sure what they do better/different than the rest of the family.
Oy, there’s so much more to write about graphing calculators.
Maybe later.
Dr. P, I was not overly concerned with standardized tests in the 1990s 😉 And as far as bringing it into class went, I made the rules.
Two players, Harry and Ted, place equal bets on who will the best of 5 coin tosses. In each round, Harry always chooses heads (H) and Ted always chooses tails (T). Suppose they are forced to abandon the game after 3 coin tosses, with Harry ahead 2 to 1. What is the fairest way to divide the pot?
mod, can you add the word “win” above, so it reads “who will win the best of 5” thanks
Harry has a 75% chance of winning, Ted has a 25% chance. That’s a fair way to split it.
squeak, please explain why you came to that conclusion.
888+88+8+8+8=1,000
~a~
I knew I should have patented my 🙂 now everyones using it 🙂
kapusta: you should know everytime i use it i think of you 🙂
Pick a number from 1-9.
Multiply it by 9.
Add the two digits together.
Subtract 5.
A=1, B=2, C=3, etc. Find the letter that corresponds to the number you ended up with.
Think of a country that begins with that letter.
Think of an animal that begins with the LAST letter of that country.
Think of a color that begins with the LAST letter of that animal.
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Sorry, but there are no orange kangaroos in Denmark.
~a~
😉 good one. i’m burning i read the bottom before i actually tried it – i wonder if i would have gotten something different. like an aqua koala in Denmark or a tangerine cat in Dominica Republic.
moish, as I was typing that, I was thinking you would read the end first. Someone once posted something that ended way down and I remember that you read the end before trying. lol!
~a~
really? i don’t remember – but yeah it’s my type.
moish how ever did you concoct an aqua koala? most random combination… 🙂
AOB the worst part is when I text or send an email or something I have to stop myself from putting it in 🙂
anyone have any more riddles that are not on Einsteins level? 🙂
moish, check out this page
http://www.theyeshivaworld.com/coffeeroom/topic/a-humorous-item/page/11
~a~
kapusta: 🙂
moish, please check out the above link that I posted for you.
Thanks in advance!
~a~
first of all that’s not a link. i had to copy and past it. and yeh i remember that. it’s like the one the teachers give out on the first day of school that say:
read all the directions first, then go back and do them.
1) draw a circle in the upper left corner of your page.
2) clap your hand four times.
…all random things till you get to the bottom one that says…
25) sit quietly with your hands on your desk and do not go back.
i never fell for those – i always read the bottom first
edit: not that anyone ever sat too quietly anyway. but you know what i mean 😉
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