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Guest Message by DevFuse
 

BMAD

Member Since 18 Feb 2013
Offline Last Active Today, 12:39 AM
*****

#333936 Creative Paradox

Posted by BMAD on 08 July 2013 - 04:13 AM

this is like my other post

 

optill02.jpg


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#333574 To-do Lists

Posted by BMAD on 28 June 2013 - 04:36 AM

who can conquer the world with aching calves?


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#332742 Crazy People

Posted by BMAD on 02 June 2013 - 04:35 AM

pino.jpg


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#332741 Crazy People

Posted by BMAD on 02 June 2013 - 04:34 AM

lookfat.jpg


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#332593 Find the common remainder.

Posted by BMAD on 27 May 2013 - 04:05 AM

480608 , 508811 , 723217. These three numbers, when divided by a certain natural number > 1 , all yield the same remainder. What is that divisor and that remainder?

 

The 'best answer' will be awarded to the person who can develop an elegant method that does not utilize brute force or code.


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#332586 Rolling a coin

Posted by BMAD on 27 May 2013 - 12:43 AM

We have two identical coins. And we roll the one on the left halfway around the other coin, so it rotates without slipping against the other coin, so that it ends up on the right of the other coin. It has rolled over a length of only half its circumference, and yet it has made one complete rotation. Which way is the head of the coin facing?


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#332585 A stand up Logician

Posted by BMAD on 27 May 2013 - 12:42 AM

Recently a self-proclaimed stand-up logician held a show with thirty people.  here is his opening dialogue:
 
 
Hello folks. It's an honor to be on Amateur Logician Night, here on the Internet. How many of you are from out-of-town? Let's see a show of hands.
 
Now, the people who raised their hands may be truth-tellers who are from out-of-town, or you may be liars who are from in-town. As the amateur logician, it is my job to determine who is really from out-of-town, and who is not. This is not an easy job, as you can well imagine.
 
If I were to ask how many of you are truth-tellers, then all of you would raise your hands. The liars would have to lie, and claim to be truth-tellers.
 
Now, let's see a show of hands, all of the people who raised your hands the first time, when I asked how many of you were from out-of-town. Very good. All of you, who now have your hands up, are from out-of-town.
 
Some of you are truth-tellers who raised your hands both times. You are from out-of-town. Some of you are liars who did not raise your hands last time. You too are from out-of-town. So, all of you who now have your hands up, are from out-of-town.
 
Thank you. Thank you. What a crowd. Thank you.

 

 

Would this approach work in identifying those that always lie and those that always tell the truth?  Why or why not?


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#332584 parallelogram conjecture?

Posted by BMAD on 27 May 2013 - 12:25 AM

Start with any general quadrilateral, and connect the midpoints of consecutive sides, making an inscribed quadrilateral as in the diagram. That inscribed quadrilateral, in the diagram, seems to be a parallelogram. Let me conjecture that this inscribed quadrilateral is a parallelogram with half the area of the original quadrilateral. Can you prove or disprove either part of my conjecture?

 


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#332583 Consecutive cubes and squares

Posted by BMAD on 27 May 2013 - 12:00 AM

Show that if the difference of the cubes of two consecutive integers is the square of an integer, then this integer is the sum of the squares of two consecutive integers.
 
(The smallest non-trivial example is: 83 − 73 = 169.  This is the square of an integer, namely 13, which can be expressed as 22 + 32.)

 


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#332576 Roads can curve too

Posted by BMAD on 26 May 2013 - 02:45 PM

A couple weeks ago, I created a question requiring the shortest path.  Now for this question, assume that roads can be curved.  We need a road that can pass through the following four cities (location of each city listed as coordinates): Los Angeles (3,4), Newport Beach (5,1), Pasadena (4,5), Santa Monica (2,3).

 

a) What's the smallest degree polynomial y=f(x) that will pass through all four cities? . . .
b) What is the exact equation of this polynomial? (Hint: use fractions not decimals)
c) Would this road go through Chatsworth at (1,6)?

 


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#332561 Reputation

Posted by BMAD on 26 May 2013 - 05:04 AM

I think someone has an issue with me.  I have been working hard to keep the forum questions alive but someone or maybe several people have gone through and have marked down every entry i have posted.  This upsets me and makes me not want to continue participating here.


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#332547 The deconstruction and reconstruction of numbers pt. 2

Posted by BMAD on 25 May 2013 - 11:13 PM

From now on, the "+" symbol no longer means to combine the count of objects (e.g. 3 things plus 4 things make 7 total things would not be modeled as 3 + 4 = 7).

 

Instead, the use of the + symbol is to show  5 + 3 = 7 to resolve the question of "how many spaces between objects are created when you line up five things and three things"

(ex: t _ t _ t _ t _ t _ t _ t _ t ) and this is now to be considered addition

 

If the other basic computational symbols maintained the same relationship to addition as they had before this new convention what would be the answers to the following problems?

 

4 - 3 = ?

 

3 x 3 = ?

 

9 / 3 = ?

 

sqrt (36) = ?


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#332546 The deconstruction and reconstruction of numbers

Posted by BMAD on 25 May 2013 - 10:52 PM

List out the numbers from 1 to 150 in a vertical column.  Left align all of the numbers to where the leading digit of the number is directly on top of the next number's leading digit

 

(e.g. for the numbers 9, 10, and 11.  9 would be above 1 and that above 1 where zero would have nothing above it and 1 below it

ex.

...

9

10

11

...

)

 

remove the nothing space above all the numbers to where the numbers are shifted up until they are at the top creating a list of new numbers.  With this new list of numbers what is the probability of randomly selecting 322? 99? and 140?


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#332542 Kissing Circles

Posted by BMAD on 25 May 2013 - 09:28 PM

If three circles are mutually tangent where one has a radius of 3cm, another has a radius of 4cm, and the last has a radius of 5cm.  What is the area of the region bounded between the three circles?


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#332541 The Age-Old Lie

Posted by BMAD on 25 May 2013 - 09:25 PM

A reporter on New Year's Eve 1993 wanted to know, from Pat and Chris, how old they were, but felt (correctly, it turns out) that one would lie. So the reporter asked them both, "Write down your age now, your age at the end of next year, add these together, then multiply the result by 5," quickly followed by: "now add the last digit of the year you were born." They had no time to fake that last digit; Pat answered 281, while Chris announced 229. Who was lying, and what were their real ages at the time?

 


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