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-   -   Some Math Teasers...... (http://auralmoon.com/forum/showthread.php?t=4663)

KeithieW 07-01-2010 03:22 PM
Some Math Teasers......
 
Not Prog related but I know there are a few people out there who could help me.

A friend, who knows of my love of Pure Maths, set me three questions. I did the first two in about 4 minutes but the third has me flummoxed. They are similar to the famous Four Fours test.

1) Using five fours and common mathematical symbols make the result 55.

2) Using three fours and common mathematical symbols make the result 55.

Easy peasy!!!

The one I'm stuck on is:

3) Using three fours and common mathematical symbols make the result 54.

Go for it Moonies.

jtmckinley 07-01-2010 05:38 PM
Re: Some Math Teasers......
 
Integer(e^4)x(4/4)

Is that cheating? :P

KenSchwartz 07-01-2010 05:46 PM
Re: Some Math Teasers......
 
Keithie,

it is trick question...sort of. i'll give you a hint...you really only need two 4's to do it.

Ken

BrianSaladSurgery 07-01-2010 06:44 PM
Re: Some Math Teasers......
 
I can do it with 4 fours

Code:
4!    4
--  •  ∑ i 
4    i=√4

Magic Mountain 07-01-2010 10:29 PM
Re: Some Math Teasers......
 
Quote:
Originally Posted by jtmckinley (Post 43692)
Integer(e^4)x(4/4)

Is that cheating? :P
You are almost right but you need to use the greatest integer function, symbol [x], which is defined as greatest integer less than or equal to a real number, so

[e^4] + 4 - 4 = 54

BrianSaladSurgery 07-02-2010 07:42 AM
Re: Some Math Teasers......
 
Thank you! Thank you! Thank you! Mr. Euler!!!

Code:
                iπ
        iπ    (e  + 4)
√4 •  (e  + 4)
This is tough to represent here without a full set of mathematical symbols.

Anyway, from Euler's Identity,

Code:
iπ
e  + 1 = 0
Therefore,

Code:
iπ
e  = -1
Thus,

Code:
iπ
e  + 4 = 3

Put this all together and you have:

Code:

√4 = 2

  3
(3)  = 27

2 • 27 = 54
Q.E.D.

In deference to Magic Mountain, as an aficionado of mathematics, a BSEE, an MSEE in Information Theory and a minor in mathematics, I just don't arbitrarily toss numbers into the trash bin. This is exact and precise math!

Magic Mountain 07-02-2010 07:52 AM
Re: Some Math Teasers......
 
Quote:
Originally Posted by BrianSaladSurgery (Post 43709)
Thank you! Thank you! Thank you! Mr. Euler!!!

Code:
                iπ
        iπ    (e  + 4)
√4 •  (e  + 4)
This is tough to represent here without a full set of mathematical symbols.

Anyway, from Euler's Identity,

Code:
iπ
e  + 1 = 0
Therefore,

Code:
iπ
e  = -1
Thus,

Code:
iπ
e  + 4 = 3

Put this all together and you have:

Code:

√4 = 2

  3
(3)  = 27

2 • 27 = 54
Q.E.D.

In deference to Magic Mountain, as an aficionado of mathematics, a BSEE, an MSEE in Information Theory and a minor in mathematics, I just don't arbitrarily toss numbers into the trash bin. This is exact and precise math!
You are just using functions like I did. My solution was very precise, you just don't like it. you used the function f(x) = e^x, I used the function f(x) = [x] =n when n<=x<n+1. Heck even multiplication is a function and so is taking roots. However, I do like your solution.

VAXman 07-02-2010 10:20 AM
Re: Some Math Teasers......
 
Quote:
Originally Posted by Magic Mountain (Post 43710)
You are just using functions like I did. My solution was very precise, you just don't like it. you used the function f(x) = e^x, I used the function f(x) = [x] =n when n<=x<n+1. Heck even multiplication is a function and so is taking roots. However, I do like your solution.
Like I said, I just don't like tossing numbers in the trash bin.

Magic Mountain 07-02-2010 10:47 AM
Re: Some Math Teasers......
 
Here's another solution:

the gamman function for n yields (n-1)! when n is an integer, so using your post above:

Gamma(4) x (sum from i=sqrt(4) to 4, of i) = 54

Magic Mountain 07-02-2010 10:52 AM
Re: Some Math Teasers......
 
Quote:
Originally Posted by VAXman (Post 43714)
Like I said, I just don't like tossing numbers in the trash bin.
or you only like bijective functions! Also using exp(pi x i) can be considered cheating as it doesn't have the number 4 in the determination, thus you could have added exp(pi x i) 42 times multiplied the result by exp(pi x i) and then added three fours. You see where I'm going with this. There are a lot of possibilities when you use a constant witout the number 4 involved.

KenSchwartz 07-02-2010 03:04 PM
Re: Some Math Teasers......
 
ok...here's one more, hinted to in my earlier post - hopefully i'll be able to format it in a readable way (or VAX will fix it for me :) )

4!
------
____
.44

so, the last 4 is clearly not needed, since .4 (repeating) is the same as .44 (repeating)

TheFish 07-03-2010 02:30 PM
Re: Some Math Teasers......
 
Quote:
Originally Posted by BrianSaladSurgery (Post 43695)
I can do it with 4 fours

Code:
4!    4
--  •  ∑ i 
4    i=√4
those are common mathematical symbols? Have not used them since college! :ick:

I'd like to see how many think a factoral is common. 8-)

Also no anger here, just playing. :-V

VAXman 07-03-2010 07:09 PM
Re: Some Math Teasers......
 
Quote:
Originally Posted by TheFish (Post 43732)
those are common mathematical symbols? Have not used them since college! :ick:

I'd like to see how many think a factoral is common. 8-)

Also no anger here, just playing. :-V
Quite common from where I come from.

KeithieW 07-09-2010 01:57 PM
Re: Some Math Teasers......
 
I solved it myself the day after I posted it but have been on holiday since so this is the first time I've been able to log in.

My solution was 4! + 4! + Gamma (4) = 54.

Thanks for all the help peeps.

VAXman 07-09-2010 04:26 PM
Re: Some Math Teasers......
 
Quote:
Originally Posted by KeithieW (Post 43767)
I solved it myself the day after I posted it but have been on holiday since so this is the first time I've been able to log in.

My solution was 4! + 4! + Gamma (4) = 54.

Thanks for all the help peeps.
As you've seen, there are many answers to this problem. It was fun though... Post some more.

progdirjim 07-09-2010 05:21 PM
Re: Some Math Teasers......
 
umm, I'm an Engineer with 4 semesters of college calculus, and I got 780 out of a possible 800 on the math SAT, and I cannot say the gamma function is "common" - but yes, fun nonetheless...

progdirjim 07-10-2010 12:49 AM
Re: Some Math Teasers......
 
jimkbrennann@gmail.com

VAXman 07-10-2010 07:48 AM
Re: Some Math Teasers......
 
Quote:
Originally Posted by progdirjim (Post 43769)
umm, I'm an Engineer with 4 semesters of college calculus, and I got 780 out of a possible 800 on the math SAT, and I cannot say the gamma function is "common" - but yes, fun nonetheless...
I won't brag about my SAT or ACT math scores. ;)

Undergrad was chock full of math: 4 semesters of (5 credit) advanced calc. (thanks to my scoring on the ACT), differential equations, vector calc., linear algebra, tensor calc., discrete statistics, continuous statistics, and applied eng. calc., and I taught the latter as a grad student. Looking back on that list, I wonder how I ever manage to get any beer drinking in. :)

I first used the gamma function in undergraduate Statistical Thermodynamics and Stochastic Processes. In graduate school, the gamma function appeared in many statistical determinations of noise in various information systems.

ProgressivePaul 07-10-2010 01:23 PM
Re: Some Math Teasers......
 
this was trippy

OverHillandDale 07-10-2010 01:33 PM
Re: Some Math Teasers......
 
Isn't the Gamma function what happens when you really piss off Dr. Bruce Banner?
http://www.qtl.co.il/img/copy.pnghttp://www.google.com/favicon.icohttp://www.qtl.co.il/img/trans.png


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