Math Is Fun Forum

ericblair

Member

Registered: 2009-11-08

Posts: 1

Take three 4's and trun into 55???

I heard about this puzzle the other day.

Take three 4's, that's 4, 4 and 4

Now perform any mathematical computation that does not introduce any new numbers and come up 55 as the answer.

You can use any mathematical expression/symbol, ie, sin 4, 4!, 4^4, etc... but only use the three 4's in that combination to get your answer.

Good luck!

billstoll

Member

Registered: 2009-11-10

Posts: 2

Re: Take three 4's and trun into 55???

that is this week's car talk puzzler.  Nice puzzle.  I came up with

(4! - sqrt(4))/(.4)

Bill

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Take three 4's and trun into 55???

very nice

leoshmu

Member

Registered: 2009-11-10

Posts: 1

Re: Take three 4's and trun into 55???

I came up with some other solutions, but I like the one you have.

Here's one
(44/4)!!!!!!=11*5=55
That's a multifactorial, n!!!!!!=n*(n-6)*(n-12)...

Here's another

44/(.4!!) =44/(.8)=55
Again, that's a double factorial, n!!=n*(n-2)*(n-4)...
If .4 is ok it seems like .4!! should be ok, but it's not as clean as the other solution

billstoll

Member

Registered: 2009-11-10

Posts: 2

Re: Take three 4's and trun into 55???

I hadn't heard of multifactorials - nice.  Those would certainly come in handy for this type of problem.

Does it make sense to use multifactorials (or factorials for that matter) on anything other than integers?  What use are they (except for problems like this one, of course!)

Assuming they are valid, the definition (n!!=n*(n-2)*(n-4)...) will have to be adjusted to cope with fractions.

.4!! is not (.4)*(-1.6)*(-3.6)...  Perhaps you intended .(4!!) which implies that decimal points are actually arithmetic operators (?).  Interesting idea :-)