Some Math Teasers......

[KeithieW]

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]

Integer(e^4)x(4/4)

Is that cheating? :P

[KenSchwartz]

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]

I can do it with 4 fours


4! 4
-- • ∑ i
4 i=√4

[Magic Mountain]

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]

Thank you! Thank you! Thank you! Mr. Euler!!!


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,


iπ
e + 1 = 0


Therefore,


iπ
e = -1


Thus,


iπ
e + 4 = 3



Put this all together and you have:



√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]

Thank you! Thank you! Thank you! Mr. Euler!!!


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,


iπ
e + 1 = 0


Therefore,


iπ
e = -1


Thus,


iπ
e + 4 = 3



Put this all together and you have:



√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]

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]

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]

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]

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]

I can do it with 4 fours


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]

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]

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]

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]

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]

jimkbrennann@gmail.com

[VAXman]

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]

this was trippy

[OverHillandDale]

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.ico (http://www.google.com/search?q=to%20)http://www.qtl.co.il/img/trans.png

[KeithieW]

For those interested the solutions I came up with for the first two were:

1) 44 + (44/4) = 55

2) (4! - sqrt4) / .4 = 55

OK, try these two.

The answers are readily available on line as they are a couple of the more difficult parts of the Four Fours puzzle but see how you get on without cheating.

1) Using four fours and common mathematical symbols make the result 113

2) Using four fours and common mathematical symbols make the result 123

Now to make you smart Alecs think a little bit more we'll say that:

a) The "log" operators are not allowed as you can get ANY positive integer by using

n = -ln[ ln( sqrt(sqrt(...(sqrt(4))...))) / ln(4) ] / ln(4)

where the number of nested sqrt() functions is twice n.


b) You may not use numeric constants (other than 4), e.g. π (pi), or e (natural logarithm base) are not allowed.

See how that floats your boats.

If it's any consolation it took me 6 months to solve these two. The solutions I came up with were the same as those suggested by David A. Wheeler who has (amazingly) produced solutions for integers 1 to 40,000!!!!!!

Enjoy!!!!