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# [Math Game] The Four Fours

Fri 27 Dec, 2013 08:49 pm
Simple little game with a deceptive challenge to it, and it'll get you thinking.

the objective is to count as high as possible within the rules, which are:

1) You have only four fours, no other numbers are allowed, so 4x3 is a no go, you cannot use 0, 1, 2, 3, 5, 6, 7, 8, or 9.

2) You must use all four fours. Make it is convoluted as you like, but four fours, no more, no less and no others as per rule one.

3) You are free to use ANY operation you like, so long as you need not write a value other than a four. it can be implied, but it may not be written. So Square root is allowed, as the 2 is not meant to be written, its just √. Cube roots are out, because you must write a 3. Fourth roots ARE permitted, because 4 is allowed.

4) Constants are out, no using Pi for example. its has an inherent value, which is not 4, so rule 1 and 3 are both violated. Its not a four and has a value of its own other than four. Factorials are permitted, they have no value if they aren't first given a number on which to operate. So ! is meaningless, but 4! has a value, so its permitted, as you only used a four.

5) While not constants, ln() and rounding operations such as floor and ceil, are considered to be outside the spirit of the challenge. Ln() permits you to have any integer value you like.

6) Rounding just makes a square peg fit a round hole by cutting off the corners. Or a round peg fit a square hole by gluing those corners on.

7) Rounding is not permitted because it is simply a notation to indicate that you have replaced the true result, with one that is approximately equal but shorter representation. The key is approximately equal, approximately is not precisely, they aren't equal. So a rounded answer, is not the answer.

8) Your answer must be the next integer in the sequence. So if 37 was last, your task is to figure out how to reach 38.

9) 44 and 444 are valid uses, as is .4 given that the zero need not be written because its implied and writing the zero has no influence on the value itself.

10) Aside from my quick set of 0-4 as a demo of how to play along, only one number per post. Multiple versions for the same number are acceptable. The idea is to avoid one person posting numbers 12 through 18 for example.

11) In line with the spirit of the previous rule, don't reply to yourself with the next number either, as then someone could provide 6 numbers in sequence on their own, which the previous rule was intended to prevent(and in part failed)

If your going to just use google and search for an answer, then don't bother. If you can't take some pride in the power of your mind, then don't demean yourself by cheating.

As mentioned in the rules, im taking on the first 5 as an example.
0 = 4+4-4-4
1 = (4/4)!^(4/4) overcomplicated on purpose. Could also just do 4/4 * 4/4, or (4+4)/(4+4)
2 = 4/4+4/4
3 = √(4*4) - 4/4
4 = √(4*4) * 4/4

Be wary of the order of operations while you're at it.

Whose up for 5?
How high can we get?
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Type: Discussion • Score: 2 • Views: 6,919 • Replies: 125

Kolyo

2
Fri 27 Dec, 2013 09:42 pm
@mars90000000,
5 = (4 * 4 + 4) / 4
mars90000000

1
Fri 27 Dec, 2013 10:56 pm
6 = 4 + √4 + 4 - 4
6 = 4!/4 + 4 - 4
0 Replies

Kolyo

1
Fri 27 Dec, 2013 11:55 pm
7 = 4 + 4 - 4 / 4
0 Replies

raprap

1
Sat 28 Dec, 2013 07:49 am
8=sqrt(4*4)+sqrt(4*4)

Rap
0 Replies

raprap

1
Sat 28 Dec, 2013 07:50 am
9=4+4+4/4

Rap
0 Replies

raprap

1
Sat 28 Dec, 2013 07:53 am
10=4!/4+4

Rap
0 Replies

raprap

1
Sat 28 Dec, 2013 07:55 am
11=4!/Sqrt(4)-4/4

Rap
markr

1
Sat 28 Dec, 2013 01:22 pm
@raprap,
12 = !4 + 4 - 4/4 subfactorials (!n) are described at http://en.wikipedia.org/wiki/Derangement
12 = (4!! + 4) * 4/4 even and odd double factorials (n!!) are described at http://en.wikipedia.org/wiki/Double_factorial
12 = (4 - 4/4)!! * 4
12 = Γ(4) + Γ(4) + 4 - 4 the gamma function is described at http://en.wikipedia.org/wiki/Gamma_function

Is ... allowed (also written with a bar over the number)? For instance, 4 / .4... = 9.
mars90000000

1
Sat 28 Dec, 2013 05:17 pm
13 = 44 / 4 + √4

Also, please don't double post! Like Rap did, but i'll let it pass this time!
0 Replies

mars90000000

1
Sat 28 Dec, 2013 05:21 pm
@markr,
No! Because it has an intrinsic value other than 4! 0.4... = 0.444444 which is NOT 0.4!

0 Replies

raprap

1
Sat 28 Dec, 2013 08:22 pm
14=4!/Sqrt(4)+Sqrt(4)

Rap
0 Replies

raprap

1
Sun 29 Dec, 2013 12:22 am
15=4*4-4/4

16=4*4*4/4

17=4*4+4/4

Rap
0 Replies

raprap

1
Sun 29 Dec, 2013 01:45 am
18=4!-4*4/Sqrt(4)

19=4!-(4+4/4)

20=4*4+Sqrt(4)+Sqrt(4)

21=4!-(Sqrt(4)+4/4)

22=4!-Sqrt(4)*Sqrt(4)/Sqrt(4)

23=4!-Sqrt(4)*Sqrt(4)/4

24=4!+(4-4)/4

Rap
0 Replies

raprap

1
Sun 29 Dec, 2013 09:34 am
24=4*4+4+4

25=4!+Sqrt(4)*Sqrt(4)/4

26=4!+4/4*sqrt(4)

Rap
0 Replies

mars90000000

0
Sun 29 Dec, 2013 10:26 am
We won't count Rap's posts after 14.

So here's 15:

15 = 4!! + 4!! - 4/4

Also, try not to use any of the solutions Rap gave for the numbers 16 through 26. Well, you can but that won't be fun!
markr

2
Sun 29 Dec, 2013 11:32 am
@mars90000000,
Seems to me that rap is just keeping this from moving at a snail's pace - especially through some of the more trivial solutions. Where's the fun in backtracking?
raprap

2
Sun 29 Dec, 2013 03:06 pm
27=4!+4/4+Sqrt(4)

28=4*4*Sqrt(4)-4

29=4!=4/4+4

30=4*4*Sqrt(4)-Sqrt(4)

Rap
0 Replies

mars90000000

0
Sun 29 Dec, 2013 06:58 pm
@markr,
Better snail's pace than no pace. if you don't like it this slow, feel free to not reply.

Meanwhile...

16=4*4*4/4
markr

2
Sun 29 Dec, 2013 08:31 pm
@mars90000000,
No pace isn't the alternative that rap is offering.

Go rap!
0 Replies

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