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blinky-
I actually love posts that don’t cause controversy.
Let’s face it- no one who posts (or lurks) here is going to change themselves because of what someone else writes, it just gets people agitated.
But I also do love riddles, it keeps my brain going, they’re a great distraction and people don’t take it personally if others have a different answer or don’t agree with the solution.
Can you solve this? It requires high school math.
post deleted as a seriously failed attempt to be humorous. we do not tolerate poor humour on this website, corny humour and puns are allowed though
Dr Pepper- yup I also noticed that you don’t post in posts that are controversial (very commendable)
However, your “high school” riddle can cause controversy, as i don’t think its on high school level:)
Moderator-80-
Yes, high school math, the function needed for the calculation is high school math (you just need to know how to apply it).
doctor
i was responding to your previous post trying to be funnily facetious
alas it appears i failed
sorry
I thought so but I didn’t want to take any chances.
Doc heres one for you (its not as sophisticated as the other ones but it kept me going for awhile…)
What comes next?
st nd rd ?
th?
1st, 2nd, 3rd, 4th
i immediately thought that the letter “a” was missing from the word “standard”
unfortunately that wasnt the question
Moderator-80-
How do you know that your answer isn’t the correct one?
Let’s wait to see what Blinky says is the correct answer.
Nice! when i got it i was like trying to figure out a whole calculation that would have made my math teacher proud and in the whole time it was pretty easy. Ok ill have to find a more sophisticated one.
doc
blinky is obviously referring to your answer
she asked what comes next, not what is missing.
maybe i can go back and edit her question to reflect my answer
kind of like how the Dubno Maggid explained why his mashulim were right on target.
A female murderer is condemned to death. She has to choose between three rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven’t eaten in 3 years. Which room is safest for her?
the lions cuz theyr dead!
yes
Dr. Pepper-
The odds that I can solve your puzzle are about the same as the odds of my being able to recite the Gettysburg Address by heart.
…backwards
…in Croatian
…while standing upside down
…underwater
…while juggling
…three running chainsaws
…with my feet
Sorry – I honestly have no idea.
I tried to find a pattern of how frequently an extra digit was added to the total as the exponent increased, but couldn’t find one.
Can I use the call-a-“squeak” lifeline?
I think posters “anon for this”, “SJSinNYC”, “ZachKessin” and “charliehall” (and possibly others) may have the background to answer your puzzle.
Feel free to use any method you want.
Let me know if you give up.
Dr. Pepper-
“Feel free to use any method you want” releases me from your “no cheating” prohibition and associated assignment (you wouldn’t be able to read my chicken-scratch handwriting, anyway), so I Googled it.
I saw something about “log”, which rings a very faint unused-for-decades bell, but no “aha!” moment, unfortunately.
You may want to keep your puzzle open a little longer for other folks who want to try it, but at this point I’m giving up.
Truth To Tell
As you journey through the black-and-white world of logic puzzles, you arrive at the inn in the town of YinYang.
The denizens of this town either tell only the truth or only lies.
Fortunately, each citizen wears a cap with an embroidered “L” if he’s a liar or a “T” if he’s a truth-teller.
Unfortunately, today is laundry day, and all the caps are in the wash.
You approach a table at which four men are seated and ask “Which of you is a truth-teller?”
Here are their answers:
Rube – “More than one”
Sy – “At least two”
Leo – “Fewer than four”
Jim – “Exactly three”
Who (if anyone) is telling the truth?
Who (if anyone) is lying?
How do you know?
(from a puzzle magazine)
Take the log (stam log is base 10) of (2^43,112,608)*((2^43,112,609)-1)
Log((2^43,112,608)*((2^43,112,609)-1)) =
Log(2^43,112,608) + Log((2^43,112,609)-1) =
Log(2^43,112,608) + Log(2^43,112,609)=
(For simplicity sake you can remove the -1 since it’s not going to make a difference anyway)
43,112,608 * Log (2) + 43,112,609 * Log (2) =
25,956,376.7
Round up to the nearest integer 25,956,377.
Ok dr. pepper, i went home and got a more sophisticated riddle for you (or a/o else)
A boss pays his worker one pound of gold each day. However he only has 7 pounds of gold that are attached. The boss can only make 2 cuts in the bar. Where should he make the cut so that his worker gets exactly whats owed to him per day???
Blinky good riddle
Day one: cut off a segment and pay them. They now have one segment.
Day three: Give them the single segment again. They now have three segments
Day four: give them the remaining piece with 4 segments and ask for all the other bits back. They now have 4 segments.
Day five: give them the single segment. They now have 5 segments.
Day 7: give them the single segment. They now have 7 segments.
Can I use the call-a-“squeak” lifeline?
I like that a lot! Pop-culture, here I come!
Dr. P- too bad I didn’t see your riddle in time, I am keen on logarithms (since back in the day, we had to use log tables (has one ever been seen in the last 40 years?) to calculate exponential equations – calculators were 4 function only).
BTW, I also noticed that you mentioned ‘e’ on the last post. Can you explain how the precise value of e was solved for? (I know why the number is important- its slope at x=0), but not how the number that has those properties was solved for).
WIY- I am impressed! Did you kow it beforehand or u really figured it out:)
Here is another one (not sure if it was posted alrady)
You have 3 canniballs and 3 whitemen that have to cross a river. They have one boat that can hold 2 ppl.
How is it that they can all get across (don’t forget that s/o has to bring the boat back) but at any time on either side there can’t be more cannibals than whitemen?
squeak-
I’m not quite sure I understand your question.
Do you want to know how e was estimated as 2.71828182845904523536 or how it fits into my sons middle name (together with pi)?
The reason why e is important is because the derivative of e^x is e^x for all x, not just where x = 0. (This property is used in building the main cables of suspension bridges.)
I guess I was too cryptic. e is important because the derivative of any exponential (say, a^x) is a^x times its derivative at x=0. If we find an ‘a’ whose derivative (i.e. slope) at x=0 is 1, then we have a nifty little function. Obviously, that ‘a’ is ‘e’. My question is, how do you go from there to finding the value of e?
e is the limit of (1 + 1/x)^x as x goes towards infinity.
Either you can use arbitrarily high numbers (the larger the number the better the approximation) or you can use a Taylor Series.
(Because the derivative of e^x is e^x, the Taylor Series is quite simple-
e = 1/0! + 1/1! + 1/2! + 1/3! + ….)
yes ive always found the Taylor series to be quite useful for such simple problems
I don’t understand the answer. I’m asking a priori, how do you arrive at that magical constant that produces an exponential function with a slope of 1 at x=0?
Moderator-80-
I knew we could agree on something. 🙂
do you want to handle squeaks question doctor, or shall i clear it up for him?
Which question?
I’m asking a priori, how do you arrive at that magical constant that produces an exponential function with a slope of 1 at x=0?
If y = a^x then y’ = a^x * ln(a).
Being that ln(x) and e^x are inverse functions of each other, ln(e) = 1.
Therefore, the slope a x = 0 is e^0 * ln(e) = 1 * 1 = 1.
Is this what you’re asking?
dont you think that is a bit oversimplified, doctor?
actually squeaks question would best be asnwered by a method of solving a set of linear equations that me and some of the boys at MIT have been working on:
A system of linear equations is homogeneous if all of the constant terms are zero:
begin{alignat}{7} a_{11} x_1 &&; + ;&& a_{12} x_2 &&; + cdots + ;&& a_{1n} x_n &&; = ;&&& 0 \ a_{21} x_1 &&; + ;&& a_{22} x_2 &&; + cdots + ;&& a_{2n} x_n &&; = ;&&& 0 \ vdots;;; && && vdots;;; && && vdots;;; && &&& ,vdots \ a_{m1} x_1 &&; + ;&& a_{m2} x_2 &&; + cdots + ;&& a_{mn} x_n &&; = ;&&& 0. \ end{alignat}
A homogeneous system is equivalent to a matrix equation of the form
Atextbf{x}=textbf{0}
[edit] Solution set
Every homogeneous system has at least one solution, known as the zero solution (or trivial solution), which is obtained by assigning the value of zero to each of the variables. The solution set has the following additional properties:
1. If u and v are two vectors representing solutions to a homogeneous system, then the vector sum u + v is also a solution to the system.
2. If u is a vector representing a solution to a homogeneous system, and r is any scalar, then ru is also a solution to the system.
These are exactly the properties required for the solution set to be a linear subspace of Rn. In particular, the solution set to a homogeneous system is the same as the null space of the corresponding matrix A.
[edit] Relation to nonhomogeneous systems
There is a close relationship between the solutions to a linear system and the solutions to the corresponding homogeneous system:
Atextbf{x}=textbf{b}qquad text{and}qquad Atextbf{x}=textbf{0}text{.}
Specifically, if p is any specific solution to the linear system Ax = b, then the entire solution set can be described as
left{ textbf{p}+textbf{v} : textbf{v}text{ is any solution to }Atextbf{x}=textbf{0} right}.
Geometrically, this says that the solution set for Ax = b is a translation of the solution set for Ax = 0. Specifically, the flat for the first system can be obtained by translating the linear subspace for the homogeneous system by the vector p.
This reasoning only applies if the system Ax = b has at least one solution. This occurs if and only if the vector b lies in the image of the linear transformation A.
I don’t mind going there but I was trying to keep this thread on a high school level.
oh okay
sometimes it hard for me to understand the workings of simple minds.
i guess ill just stay out of this discussion then
e is the limit of (1 + 1/x)^x as x goes towards infinity
How did you arrive at this equation is my question.
I skipped high school.
By the way, we already discussed this way back in the olden days when ICOT asked me to teach him Cramer’s Rule.
“i skipped high school”
not me
the state wouldnt allow it
but they let me teach the advanced high school physics course instead of attending as a student.
the students couldnt believe that such a knowledgeable 10 year old was actually cool and not nerdy!
We didn’t have states in those days
squeak-
Take compound interest for example:
Compounded once per year => (1 + 1/1)^1
Compounded twice per year => (1 + 1/2)^2
Compounded three times per year => (1 + 1/3)^3
Compounded four times per year => (1 + 1/4)^4
Compounded twelve per year => (1 + 1/12)^12
.
.
.
Compounded continuously => (1 + 1/x)^x as x goes to infinity.
That proves that continuous interest can be computed as e^r. What does that have to do with my question? If I’m not making sense, forget it.
BTW, blinky, I apologize for completely hijacking this thread and causing your riddle to be ignored. Here is a solution:
I have taken the liberty of changing the demographics a bit to fit my sensibilities (Joseph would understand).
1) 2 Cannibals (C) take the boat across the river.
2) 1 C heads back
3) 1 C and 1 Marauding Imperialist (MI) take the boat across the river.
4) 1 C heads back
5) 2 MI take the boat across the river
6) 1 C takes the boat back
7) 2 C take the boat across the river
8) 1 C heads back
9) 2 C take the boat across the river
10) The Marauding Imperialists instruct the scribe to omit from the story any mention of the revolvers, rifles, and bayonettes they were carrying so as to misdirect the reader’s sympathy. It’s just a small band of harmless white guys now, scared to death of the vicious cannibals.
squeak–
You’re already quite pop in the CR culture.
blinky
Thanks for actually posting one that normal folks can try.
OK, we have three canibals and three tourists on the west side of the river, needing to cross to the east bank in a two-person canoe.
There can never be tourists on the same side of the river as a larger number of canibals.
C = canibal
T = tourist
W = west side of river
E = east side of river
1) 2 canibals cross together
result – e=3t,1c w=0t,2c
2) 1 canibal comes back alone.
result – e=3t,2c w=0t,1c
3) two canibals cross together
result – e=3t,0c w=0t,3c
4) 1 canibal comes back alone.
result – e=3t,1c w=0t,2c
5) two tourists cross together
result – e=1t,1c w=2t,2c
6) 1 tourist and 1 canibal come back together.
result – e=2t,2c w=1t,1c
7) two tourists cross together
result – e=0t,2c w=3t,1c
8) 1 canibal comes back alone.
result – e=0t,3c w=3t,0c
9) two canibals cross together
result – e=0t,1c w=3t,2c
10) 1 canibal comes back alone.
result – e=0t,2c w=3t,1c
11) two canibals cross together
result – e=0t,0c w=3t,3c
Squeak-
I’d love to answer your question but I honestly don’t understand it.
Can you try explaining it in different words?
ICOT- Sorry wrong answer- 3) 1 C and 1 Marauding Imperialist (MI) take the boat across the river.
That means that there are 2C’s and one MI are on that side- no good
icot does not make mistakes
I’ll try.
If I asked you what the value of Pi is, you would say it is 3.1415926…….. If I asked you how the value of Pi was obtained, the answer would be to measure a circle of any size and divide the circumference of the circle by its diameter.
What’s happening here is I am asking you how the value of e was derived and you are telling me what the value is (in numerical and algebraic form).
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