4 4s - a game

fjon

Saw this on another forum, thought it sounded like fun. The idea is to count up through the numbers (1,2,3,4, etc) using only 4 4s. So for example, I would start with:

0 = 4-4+4-4
1 = 4/4+4-4

Anyone want to continue it?

Yakuza

2 = 4/4 + 4/4
3 = (4+4+4)/4

(Now I'm stuck!!)

Is it the number 4 you must use, or the digit 4? i.e is
7 = 44/4-4 valid?

graphene

4 = √(4*4*4/4)
5 = (4/4) + √4 + √4

ecksor

What operations and functions can be used?

Yakuza

I had assumed that we could only use +, -, *, ÷.
Can we use exponents, roots, decimals, recurring decimals, uhm...factorials...err...logs...trig functions?

How far did they get in the other forums you mentioned, fjon?

Tar.Aldarion

we have to use roots etc from the ones i have done before.
fjon will you allow this!

randomname2005

Here is the FAQ for the 4 4s problem.

http://www.geocities.com/TimesSquare/Arcade/7810/44sfaq.htm

although there may be slightly different versions
R

fjon

Last time I looked they were up to 58 in the other thread. It is the digit 4, and not number 4 that is to be used, so 44 is acceptable.
Thanks for the link randomname2005. According to it, the following are and are not allowed:

Based on the above problem statement and the 8 examples, here's what I believe is allowed in this version of the puzzle:
Unlimited addition, subtraction, multiplication, division, or squaring of operands, although only squaring is ever needed more than once on a single operand
Parentheses as necessary to clarify order of operations
The use of 4 factorial (4!=24) as an initial operand
The use of repeating decimal 4 (.4~=.444…) as an initial operand (that uses up only one of your 4 fours)
"gluing" together of multiple fours, e.g. 44, 444, and 4444, with the possible insertion of a decimal point

What isn't allowed (some of which is conjecture):
any other operations (square root, log, ln, exponentiation (xy), %, etc.) not specifically allowed
factorial of anything besides 4
the "+/-" key, although negative values can be obtained by inserting a leading "-"
using more or less than four 4s
using symbolic numbers like π or e

Anyway:

6 = ((4+4)/4)+4

fjon

In the other thread they did have to resort to using Roots, SQRT, and ^, so if you get stuck you can use them too, even though not accepted in the "rules" above.

fjon

Yakuza wrote:

7 = 44/4-4

.

Nosh*tsherlock

8 = 4+4+4-4
9 = (4/4)+4+4

Nosh*tsherlock

10 = (44-4)/4

Yakuza

A few more...

11 = 44/(√4 + √4).
12 = (4+4) + √4 + √4
13 = 44/4 + √4
14 = (4*4) - 4 + √4
15 = (4*4) - 4 / 4
16 = (4*4) - 4 + 4
17 = (4*4) + 4 / 4
18 = (4*4) + 4 / √4

fjon

Nice one Yakuza!

19=4!-4 - (4/4) (Unless someone can think of another way?)
20=4*(4+(4/4))

Mary-Ellen

If factorials are allowed
21 = 4! - (4 - ( 4 / 4 ) )
22 = 4! -( (4 + 4) / 4 )

Yook

I'm supposed to be studyin.
Im hooked now.

Mary-Ellen

Totally addicted too.

23 = 4! + (sqr4 + sqr4)/4
24 = (4*4) + 4 + 4
25 = 4! + sqr4 + (4/4)
26 = 4! + (4 * 4)/4
27 = 4! +4 - (4/4)
28 = (4 * 4 * sqr4) - 4

Yook

29 = 4! + 4 + (4/4)
30 = 4! + sqroot 4 + sqroot 4 + sqroot 4

Nice job with 23 btw, but its - not +.

Ishmael

31 = (4 - 4/4)^3 + 4

Edit: probably outside the rules?

Yook

31 = (4! + (4 + sqroot 4)! ) / 4!
32 = 4*4 + 4*4

Yook

Ishmael wrote:

31 = (4 - 4/4)^3 + 4

Edit: probably outside the rules?

Yea, sorry man its 4 4's only.

fjon

How about we skip 33? Also 35, 37, 39 and 41 seem impossible.

34 = 4!+4+4+SQRT(4)

Yakuza

If we allow squaring (as it's a 1-button function on most calculators (for which this was originally designed), then it makes it easier...)

33 = 4²+4² +4/4
35 = (4+√4)² - 4/4
36 = (4+√4)² - 4 + 4
37 = (4+√4)² + 4/4
38 = (4+√4)² + 4/√4
39 = 4!+4² - 4/4
40 = 4!+4² - 4 + 4
41 = 4!+4² + 4/4
42 = 4!*√4 - 4 - √4
43 = 44 -4/4
45 = 44 +4-4
45 = 44 +4/4

That's enough for now

nanook

its amazing what you like, was just browsing and i had to have a go sorry if its closed but i have a question

what is 4! dont remember that when i was doing sums in school


46= 4(4*(4+4+sqr4) + ((4*4*4)-(4*4)/(4+4))

Yakuza

4! (reads as "4-factorial") is basically shorthand for 4 * 3 * 2 *1.

Or more generally,
n! = n*(n-1)*(n-2)*...*3*2*1.

By convention, 0! =1.

It's used heavily in combinatorics / probability theory, where you are counting ways things can be combined.

More info here: http://www.algebra.com/algebra/about/history/Factorial.wikipedia

Moogle

nanook wrote:

its amazing what you like, was just browsing and i had to have a go sorry if its closed but i have a question

what is 4! dont remember that when i was doing sums in school


46= 4(4*(4+4+sqr4) + ((4*4*4)-(4*4)/(4+4))

Thought only 4 4s were allowed.

46 = 44 + 4/√4
47 = 4! + 4! - 4/4
48 = 4! + 4! - 4 + 4
49 = 4! + 4! + 4/4
50 = 4! + 4! + 4/√4

Moogle

Took a while:

51 = ((4! - √4)/.4) - 4

4Xcut

52=4!+4!+√4+√4

Tar.Aldarion

53=(√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4+√4)/√4

wait you said only four fours...

Tar.Aldarion

53=4!+4!+√4/.4
54 =4!+4!+4+√4
55 =(4!-4+√4)/.4

Moogle

56 = 44 + 4² - 4
57 = ((4 - √4)/.4) + √4
58 = 44 + 4² - √4
59 = ((4 - √4)/.4) + 4
60 = 4 x (4² - 4/4)

Moogle

61 = (4!/.4) + 4/4
62 = (4!/.4) + 4/√4
63 = 4² x 4 - 4/4
64 = 4² + 4² + 4² + 4²
65 = 4² x 4 + 4/4
66 = (4!/.4) + 4/4
67 = (4! + √4)/.4 + √4
68 = (4!/.4) + 4²/4
69 = (4! + √4)/.4 + 4
70 = (4!/.4) + 4/.4

X-SL

71 = 4.(4+4)+4 . 4/root4-4/4

not sure if that's right. ah well

Tar.Aldarion

71 = (4!+4.4)/.4
72 = 44+4!+4
73 = (4! C sqrt 4)/4 + 4 (using nCr)
74 = 4!+4!+4!+sqrt 4
75 = (4!+4+sqrt 4)/.4
76 = (4!+4!+4!)+4
77 = ((4 - gamma(sqrt4))^4 ) - 4(4/.4repeating)^sqrt4 - 4 does this count as four fours....hmmm
78 = 4*(4!-4)-sqrt 4
79 = 4!+(4!-sqrt 4)/.4
80 = (4*4+4)*4

EamonnKeane

81 = 4 x 4 x 4 + (4 squared)

Moogle

EamonnKeane wrote:

81 = 4 x 4 x 4 + (4 squared)

That'd be 80.

Try:

81 = (4² (?4) + .4)/.4

Tar.Aldarion

82 4*(4!-4)+sqrt 4
83 (4!-.4)/.4+4!
84 44*sqrt 4-4
85 (4!+4/.4)/.4
86 44*sqrt 4-sqrt 4
87 4 x 4! - 4 / 0.bar4 or 44*sqrt(4)-i^4 or ((4 - gamma(sqrt4))^4) + (gamma 4)
88 4*4!-4-4 or 44+44
89 4!+(4!+sqrt 4)/.4
90 4*4!-4-sqrt 4
91 4*4!-sqrt 4/.4
92 4*4!-sqrt 4-sqrt 4

Tar.Aldarion

93 4*4!-gamma(4)/sqrt 4 or (4! C sqrt 4)/4 + 4!(using nCr)
94 4*4!+sqrt 4-4
95 4*4!-4/4
96 4*4!+4-4 or 4!+4!+4!+4!
97 4*4!+4/4
98 4*4!+4-sqrt 4
99 44/.44(repeating) or 4*4!+gamma(4)/sqrt 4 or 4/4% - 4/4
or (4 * 4!) + sqrt (4)/sqrt(.0 bar 4)
100 4*4!+sqrt 4+sqrt 4

*Angel*

Just a general comment, since when has .4 been allowed in this?

The Rules: don't have it included.

Just wondering.

Toy

101 = ((4^2)/.4 + .4)/.4
102 = 4!x4 + 4 + sqrt4

JC 2K3

*Angel* wrote:

Just a general comment, since when has .4 been allowed in this?

The Rules: don't have it included.

Just wondering.

Square roots aren't allowed either.........

Tar.Aldarion

*Angel* wrote:

Just a general comment, since when has .4 been allowed in this?

The Rules: don't have it included.

Just wondering.

It is allowed, they use in themselves in the examples they give, which are in fact 1 -100 :eek:
Oh and the guy that started the thread said we could use square roots if we needed. There is conjecture on whether they should be allowed!

nitroboy

bit longwinded and simplistic, but does the job!!

103 (4*4*4*SQR4)- (4*4+4+4+((SQR4/4)*SQR4)))
104 (4*4*4*SQR4)- (4*4+4+4)

woops only spotted 4 fours are only allowed, ah well better start thinking outside the box!!!