(I posted this at another site. I'm looking for any takers here. Ignore that "1." symbol below, not the instructions, though.)
Arithmetic - - Use four 4's to make 5 with limitations
Arithmetic - - Use four 4's to make 5 with limitations
- Make an expression using exactly four 4's and no other digits.
In order to reduce the number of solutions, I am requesting the following list of limitations.
You can use:
up to two addition signs
no subtraction/negative signs
up to one multiplication sign, "*"
up to one division sign, "/" for a horizontal expression, or instead, use one horizontal fraction bar
no concatenation
up to one pair of parentheses (not including those for "sqrt(X)" form)
no exponentiation
up to three square root symbols
no other roots
no decimal points/no repeating decimals
no factorial symbols of any type
no other functions or characters
- - - - - - - - - - - - - - - - - - - - - - - - - -
For the sake of limiting solutions, these forms within a solution, or the solution itself, will be considered the same:
A + B =
B + A
- - - - - - - -
A(B + C) =
(B + C)A =
A(C + B) =
(C + B)A
- - - - - - -
A/B + C =
C + A/B
- - - - - - - -
etc.
If you would like to write the square root of 4 in your expressions, you may want to type [FONT=MathJax_Main-Web]√[/FONT]4 using Latex, or "sqrt(4),"
or maybe there is the square root sign in a handy menu on this page/site.
not sure.
To get a couple of examples out of the way, I am starting off the list of solutions with:
[FONT=MathJax_Main-Web]√[/FONT](4∗4) + 4/4 = 5
[FONT=MathJax_Main-Web]√[/FONT]4∗[FONT=MathJax_Main-Web]√[/FONT]4 + 4/4 = 5 . . . . . . . . . which is just a variant of the one above it
We could keep a running list of solutions.
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