Four Fours

[petrw1]

I don't know if this a new one for some of you OR as old as Mersenne himself

The Four 4's Puzzle: For you Disney fans this puzzle is also known as: "The 101 Damn Calculations". Using four 4's and standard mathematical operations formulate equations with the answer being each of the numbers from 0 to 100. All 101 (a prime number!!!) are possible.

Every calculation MUST use exactly four 4's and no other digits.
The allowable operations are:
· Addition: 4 + 4 = 8
· Subtraction: 4 – 4 = 0
· Multiplication: 4 * 4 = 16
· Division: 4 / 4 = 1
· Parenthesis: (4 + 4) / 4 = 2
· Factorial: 4! = 24
· Exponential: 4^4 = 256
· Square-root: √4 = 2
· Concatenation: 44
· Decimal Point: .4
· Repeating Decimal .4 (uses one 4) repeating is equal to 4/9

Examples:
4+4-4-4 = 0
4!*4*(4/4)= 100

[DJones]

Originally Posted by petrw1

Examples:
4+4-4-4 = 0
4!*4*(4/4)= 100

Doesn't 4!*4*(4/4) actually equal 96?
(4! + 4/4) * 4 = 100

[petrw1]

Originally Posted by DJones

Doesn't 4!*4*(4/4) actually equal 96?
(4! + 4/4) * 4 = 100

So embarassed...

That should have said 4! * 4 + SQR(4) + SQR(4) = 100
Your answer is good too.

[Wacky]

Please see thread 4756

[petrw1]

Originally Posted by Wacky

Please see thread 4756

I did check the puzzles forum before I sent this in but didn't find it...

Anyway, sorry for having to ask but how do I go to a specific thread?

Thanks

[Uncwilly]

Here is that thread easy style:
http://www.mersenneforum.org/showthread.php?t=4756

Notice the form of the url, the t= is the thread number. If it were p= , that would be a post number.

[mfgoode]

Originally Posted by Uncwilly

Here is that thread easy style:
http://www.mersenneforum.org/showthread.php?t=4756

Notice the form of the url, the t= is the thread number. If it were p= , that would be a post number.

Thank you Unwilly for the info as I often wondered about this too.
But where do you get t=4756 from? Is it from the archives?
Mally

[petrw1]

OKAY...I concede. I was reminded that this puzzle ran a couple years ago....albeit with slightly different parameters....so watch for a companion posting of the Four Nines puzzle....

[Andi47]

Originally Posted by Wacky

Please see thread 4756

This was not the same. In thread 4756, it was allowed to use less than four fours, the "square" operator was allowed (but no SQRT, no exponent)

Here you have to use EXACTLY four fours and a different set of allowed operators. It would be fun to see how far we could complete the list according to the rules in this thread. (a number of things used in thread 4756 would not work here)

Note: squaring seems to be still allowed using x^2 = x^(√4)

let's start with a somewhat "unusual" 1:

1=(4!-4)^(4-4)
3=4-4^(4-4)
5=4+4^(4-4)

[Wacky]

And just to keep it "interesting", no skipping around. :)
You have to wait to post "7" until someone posts a solution for 6", etc.
Posting "better" solutions for smaller numbers is fine.

And, since this is abour 4's, no more than 4 additions before you give others a chance to play.

0 = 4 + 4 - 4 - 4
1 = (4+4)^(4-4)
2 = 4/4 + 4/4
3 = 4-4^(4-4) (from Andi47)
4 = 4*4^(4-4)
5 = 4+4^(4-4) (from Andi47)

[DJones]

Well, as the rules are subtly different, I'll join in.

6 = 4 + ((4 + 4) / 4)
7 = 4 + 4 - (4 / 4)
8 = 4 * 4 - 4 - 4
9 = 4 + 4 + (4 / 4)

I appreciate that some of the brackets are redundant, but I believe in making things as clear to comprehend as possible.