Denoting recurring numbers in formulas

[Guest]

How can you dentote a recurring number in an Excel formula eg something like
2/.4~ =3
Would appreciate any solutions to this please.

 

[Faz]

JayBea, what exactly do you mean by this?

2/.4~ =3

If you mean something like 0.33333333 and so on, you can put 1/3

From what i see, you're saying 2/0.444444... but that would be 4.5, no
3

 

[Guest]

JayBea, what exactly do you mean by this?

2/.4~ =3

If you mean something like 0.33333333 and so on, you can put 1/3

From what i see, you're saying 2/0.444444... but that would be 4.5, not
3.

Sorry My mistake on the formula I was thinking of the final result I was
intending which was the sqrt(4)/sqrt(0.4444444)=3 and summarised the formula
a little too much

The question is asked because of notating the problem of The Four Fours in
Excel where the only digit you can use is the number 4 and no more or less
than four times in the formula. This is why I was looking for the notation
for a recurring number, in order to only use the digit "4" once by denoting
it as recurring.
eg the formula (Fact(4)*4)+(sqrt(4)/sqrt(.4444444))=99 and would be correct
but for the fact there are more than Four Fours in it.

 

[Dana DeLouis]

the sqrt(4)/sqrt(0.4444444)=3

The function Rept might help, although I don't see a solution for this
problem because you want 0.4444444
=--REPT(4,4)

returns the number 4444.

The best I got so far was...

=SQRT(4)/SQRT(4/((4+4+4/4)))

but it has 6 4's.
since 0.444... equals 4/9

But, the above equation does reduce to =SQRT(4+4+4/4) to return 3.
HTH :>)

 

[Dana DeLouis]

The question is asked because of notating the problem of The Four Fours...

1)

intending which was the sqrt(4)/sqrt(0.4444444)=3 and summarized the
formula
2)
eg the formula (Fact(4)*4)+(sqrt(4)/sqrt(.4444444))=99 and would be
correct
but for the fact there are more than Four Fours in it.

Hi. A little off topic I know, but I see you are trying to only use the
functions (+ - * / ^ ! Sqrt) on (4,4,4,4) (Four 4's)

1)
There was an interesting Journal article about a year ago on "Algebraic
Programming." It was referencing another programming language.
In short, if we freeze such things as Communative and Associative laws, etc,
I count 273 solutions that total 3.

Here are just 5 of the 273 that total 3 picked at random:
=FACT(4)/SQRT(4)/SQRT(4)/SQRT(4)
=(FACT(4)+FACT(4)+FACT(4))/FACT(4)
=(4+SQRT(4)) / (4-SQRT(4))
=(4/4)^SQRT(4)+SQRT(4)
=4-FACT(4)^(FACT(4)-FACT(4))

2)
However, I am not showing any solutions for 99.
For 98, I count 52. ie

=4*FACT(4) + 4/SQRT(4)
=(4+FACT(4)*4)-SQRT(4)

and for 100, I count 99 solutions.
ie =4*(FACT(4)+FACT(4)/FACT(4))

However, I'm showing nothing that totals 99.

Good luck. Might be interesting to add more functions in the list to
examine.

 

[Guest]

Thanks for the replies Dana

I did manage to get 99 with a bit of a cheat, by using Fact(.4) in the
formula as Excel produces the answer of 1 which applies for any number below 2

eg. =FACT(4)*4+SQRT(4)+FACT(0.4)
or=FACT(4)*4+4-FACT(0.4)

OK it is a huge cheat, I Know, but it does get Excel to provide the right
answer

I would love to see an Excel math function for recurring numbers in the next
edition just to be able to overcome this problem without cheating, but then
again there isn't even a SQRT button on the MS scientific calculator yet

 

[Dana DeLouis]

Fact(.4). That's a cleaver idea. :>)

Ok. Here's my idea for a repeating 4 then.

=SQRT(4)/SQRT(--("." & REPT(4,44)))

Which equal 3. :>)

 

[Dana DeLouis]

Ok. Another cheat... :>)
=(FACT(4)+SIGN(4))*4-SIGN(4)

FACT(0.4) can be interpreted by some other programs as the Gamma function,
with a numerical value of 0.8873 (ie Gamma(1.4) )

This is an interesting programming challenge due to the many combinations.
It needs checks also because something simple as 4^4^4 has 155 digits.
Excel can only read this Left To Right, so arrives at a non-standard
interpretation of 4294967296. Anyway, very interesting... :>)