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# Using Four 4's and Operations...

0
384
6

How far can we get?

Here are the rules:

Use four 4's and operators (+,-,*,/,!,^, and square roots, concatenation) to get whole numbers. We can only go in order.

$$0={(4-(\sqrt4}*\sqrt4))^{4!}$$

$$1=\frac{44}{44}$$

See if you can get 2 and then 3 and then 4 and then 5 and so on...

Guest May 19, 2017
#1
+7339
+2

I am not very good at these.....but here's ones for 2 and 3 and 4:

2 = $$\frac{4*4}{4+4}$$

3 =  $$\sqrt{4}+\sqrt4-\frac44$$

4 = $$4! - 4*4 - 4$$

Also...what do you mean by concatenation?

I looked it up but I still don't really know what it is

*edit*

I accidentally put 5 fours for 2...thanks to geno for letting me know!!

hectictar  May 19, 2017
edited by hectictar  May 19, 2017
edited by hectictar  May 19, 2017
#2
+1

Good job, hectictar!

Concatenation means the action of linking together. For example, 44 is a concatenation, or a link, of a 4 and another 4. Makes sense, no? It's an easier concept to explain than to say the vocab word...

Anyway, here comes the next few.

$$5=\sqrt4+\sqrt4+\frac{4}{4}$$

$$6=\frac{4!}{4+4}*\sqrt4$$

Guest May 19, 2017
edited by Guest  May 19, 2017
#3
+7339
+1

Ah okay..thanks for the explanation!

Here's a 7, 8, and 9...(...These ones seemed a little too easy  )

$$7=4+4-\frac44 \\~\\ 8=4+4*\frac44 \\~\\ 9=4+4+\frac44$$

hectictar  May 19, 2017
#4
+2294
0

$$10=4+4+4-\sqrt4$$

$$11=\frac{44}{\sqrt4^{\sqrt4}}$$

$$12=\sqrt4(\sqrt4+\sqrt4+\sqrt4)$$

TheXSquaredFactor  May 19, 2017
#5
+92650
+1

Here's some more   (without concatenation )

4! / √4   -  4 / 4   =    24 / 2  -  1   =    12  -  1    =   11

4! / √4  + 4/4   =   24/2  + 1   =  12 + 1  =  13

4! / √4   + 4 / √4   =   24/2  + 4/2  =  12  + 2  = 14

4*4  - 4/4    =  16 - 1   = 15

4 + 4 + 4 + 4  = 16

4 * 4   +   4/4    =   16 + 1  = 17

4 * 4   + 4 / √4  =  16   + 4/2   =   16  + 2    =  18

4!  - 4  -  4/4   =   24  - 4 - 1   =   19

4!/√4  + 4 + 4   =   24/2 + 4 + 4  =  12 + 4 + 4   = 12 + 8 =  20

4! - 4 + 4/4  =   24  - 4  + 1   =  20 + 1  =  21

4! -  4 + 4/√4   =  24 - 4 + 4/2  =  24 - 4 + 2   =  20 + 2  = 22

4! -  (√4 *√4) / 4   =  24 - (2 *2)/4  =  24 - 4/4  = 24 - 1 = 23

4! - 4/√4  + √4  =   24 - 4/2 + 2  =   24  - 2  + 2   =  22 + 2  =  24

CPhill  May 19, 2017
#6
+1

I guess that I will continue the trend, but my answers aren't too creative...

$$26=4!+\sqrt{4}+4-4$$

$$27=4!+\sqrt{4}+\frac{4}{4}$$

$$28=4!+\sqrt{4}+\frac{4}{\sqrt{4}}$$

$$29=4!+4+\frac{4}{4}$$

$$30=4!+4+\frac{4}{\sqrt{4}}$$

Guest May 19, 2017