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# Mathematical question to tease your brain

metalfreek
All right guys here is a question. You have to form each of these numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15, 16, 17, 18, 19 and 20 by using 4 just four times by combining with any mathematical symbols like + - / * or square root etc.

For example here are few

(i) (4/4)-(4/4)=0
(ii) 44/44=1
(iii) (4/4)+(4/4)=2
(iv) (4+4+4)/4=3
(v) 4+4-sqrt(4)-sqrt(4)=4

Now you have to complete the remaining ones. Remember you have to use 4 four times.
The real riddle does not allow square root, or turing two fours into 44 as far as i know
infinisa
Hi metalfreek

We've seen this problem before on another thread - The sixes problem.

Here are the answers I have so far:

4/4 + 4 - 4 = 1
(4 x 4)/(4 + 4) = 2
(4 + 4 + 4)/4 = 3
√4 + √4 + 4 - 4 = 4
√4 + √4 + 4 /4 = 5
4 + 4 - 4 + √4 = 6
4 + 4 – 4/4 = 7
4 + 4 + 4 - 4 = 8
4 + 4 + 4/4 = 9
4 + 4 + 4/√4 = 10
44/4 = 11
4 + 4 + 4 = 12
44/4 + √4 = 13
4 + 4 + 4 + √4 = 14
4 x 4 - (4/4) = 15
4 x 4 = 16
4 x 4 + 4/4 = 17
4 x 4 + √4 = 18
floor(4.4 x 4 + √4) = 19
4 x 4 + 4 = 20

Like LukeakaDanish, I think you need to be clearer about the "rules of game", which I think allow you to use up to 4 4 's (I've used fewer in some cases above).
metalfreek
Let me explain the rules one more time
(1) You have to use 4 four times to obtain a number.
 Quote: 4 x 4 + 4 = 20 44/4 = 11 4 x 4 = 16
These are wrong because you have used 4 three times only.

(2) You can use combination of 4 like 44 or 444.

(3) You can use square root as well.
infinisa
metalfreek wrote:
Let me explain the rules one more time
(1) You have to use 4 four times to obtain a number.
 Quote: 4 x 4 + 4 = 20 44/4 = 11 4 x 4 = 16
These are wrong because you have used 4 three times only.

(2) You can use combination of 4 like 44 or 444.

(3) You can use square root as well.

I guess I'll have to redo 11, 12, 16, 18 and 20:
floor(44.4/4) = 11
4 + 4 + √4 + √4 = 12
4 + 4 + 4 + 4 = 16
4 x 4 + 4 - √4 = 18
4 x 4 + √4 + √4 = 20

Is that OK now?
I don't think you can do "floor"
infinisa
 LukeakaDanish wrote: I don't think you can do "floor"

May be, but I'd like to hear metalfreek's opinion on this - he makes the rules on this one
metalfreek
The mathematical operation that you can use is
(2) Subtractions
(3) Multiplication
(4) Division
(5) Square root

Thats all you can use. And you have to use 4 four times in order to obtain all numbers.
infinisa
 metalfreek wrote: The mathematical operation that you can use is (1) Addition (2) Subtractions (3) Multiplication (4) Division (5) Square root Thats all you can use. And you have to use 4 four times in order to obtain all numbers.

I guess I'll have to reredo 11 and 19:
√4 x √4 / .4(.) + √4 = 11
4 x 4 + √(4/ .4(.)) = 19

Here I must explain that by .4(.) I mean "point four recurring", normally written with a dot above the 4:
 Code: . .4

and is equal to 4/9.

Is that OK now?
You're still using a tool you're not allowed to use.

The 11 one can be done this way:

(4^3 - 4^2 - 4)/4

or this way:

(4 x 4) - 4 - 4^0
infinisa
 LukeakaDanish wrote: You're still using a tool you're not allowed to use. The 11 one can be done this way: (4^3 - 4^2 - 4)/4 or this way: (4 x 4) - 4 - 4^0

I thought you were only allowed to use 4 4's and no other numbers? If you use other numbers the problem becomes trivial.

As to whether I'm "still using a tool you're not allowed to use", let's hear what metalfreek has to say
metalfreek
You cannot use any other numbers except 4.
 Quote: Let me solve another one for you (44+4)/4=12 4*4+sqrt(4)+sqrt(4)=20 (44/4)+4=15
infinisa
Hi metalfreek

Are my latest solutions OK?
Quote:
I guess I'll have to reredo 11 and 19:
√4 x √4 / .4(.) + √4 = 11
4 x 4 + √(4/ .4(.)) = 19

Here I must explain that by .4(.) I mean "point four recurring", normally written with a dot above the 4:
 Code: . .4

and is equal to 4/9.

Is that OK now?
infinisa wrote:
 LukeakaDanish wrote: You're still using a tool you're not allowed to use. The 11 one can be done this way: (4^3 - 4^2 - 4)/4 or this way: (4 x 4) - 4 - 4^0

I thought you were only allowed to use 4 4's and no other numbers? If you use other numbers the problem becomes trivial.

As to whether I'm "still using a tool you're not allowed to use", let's hear what metalfreek has to say

Well, square root is the same as ^(1/2)...so surely diferent powers are ok?
metalfreek
infinisa wrote:
Hi metalfreek

Are my latest solutions OK?
Quote:
I guess I'll have to reredo 11 and 19:
√4 x √4 / .4(.) + √4 = 11
4 x 4 + √(4/ .4(.)) = 19

Here I must explain that by .4(.) I mean "point four recurring", normally written with a dot above the 4:
 Code: . .4

and is equal to 4/9.

Is that OK now?

I will solve 11 as
(4/.4)+(4/4)=11 but your solution is also right.

Regarding obtaining 19
4 x 4 + √(4/ .4(.)) = 19 this is right.

I think this question is solved if you want another one than I can post another here.
infinisa
 metalfreek wrote: I think this question is solved if you want another one than I can post another here.

I suggest you create a new topic, though.

Thanks for the fun problem.
Afaceinthematrix
 infinisa wrote: √4 + √4 + 4 - 4 = 4 Like LukeakaDanish, I think you need to be clearer about the "rules of game", which I think allow you to use up to 4 4 's (I've used fewer in some cases above).

If you can use fewer than four 4's, then why go through all that work to get four? You can just use 4=4 and be done...

P.S. Would log_4(4) + log_4(4) = 2 be legit? I assume that it is because logs weren't banned, but I'm not sure if they're allowed (just like in the sixes problem where I used (log10 + log10 + log10)!=6... I didn't know if I could do that). The _4 means "base four." I wasn't sure how to represent that on a forum without subscripts.
Afaceinthematrix
 metalfreek wrote: The mathematical operation that you can use is (1) Addition (2) Subtractions (3) Multiplication (4) Division (5) Square root Thats all you can use. And you have to use 4 four times in order to obtain all numbers.

Ahhh... no logarithm base 4? No floor function either? That's a mathematical operator (it's usually called greatest integer function).
metalfreek
I have created a new thread here http://www.frihost.com/forums/vt-106519.html I hope you like the the new question.
socceraggie
metalFreak,

I know you made the rules for this challenge, but isn't the solution you suggested for obtaining 19 incorrect.

 Quote: Regarding obtaining 19 4 x 4 + √(4/ .4(.)) = 19 this is right.

The use of .4(.) is technically using more than one 4. It would be using an infinite number of fours. If you were to convert this into a fraction, you would be stuck using a 9 (such as 4/9).

Just curious of how this does not break one of the rules.

Thanks!
Dennise
(4+4+sqrt(4))/sqrt(4) = 5
kaitou1412
 metalfreek wrote: All right guys here is a question. You have to form each of these numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15, 16, 17, 18, 19 and 20 by using 4 just four times by combining with any mathematical symbols like + - / * or square root etc. For example here are few (i) (4/4)-(4/4)=0 (ii) 44/44=1 (iii) (4/4)+(4/4)=2 (iv) (4+4+4)/4=3 (v) 4+4-sqrt(4)-sqrt(4)=4 Now you have to complete the remaining ones. Remember you have to use 4 four times.

sqrt(4)*sqrt(4)+4/4 = 5
sqrt(4)*(4-4/4)=6
4+4-4/4=7
4*sqrt(4)*(4/4) = 8
(sqrt(4)+4/4)^sqrt(4) = 9
sqrt(4)*(4+4/4) = 10
4!/sqrt(4)-4/4 = 11
(4/4)(4!/sqrt(4)) = 12
4!/sqrt(4)+4/4 = 13
4x4-4+sqrt(4)=14
4x4-4/4 = 15
sqrt(4x4x4x4) = 16
4x4+4/4 = 17
4!/sqrt(4)+4+sqrt(4)=18
4!-(4+4/4)=19
4x(4+4/4)=20