Elementary math that professors cant solve

In summary: I remember in my grade school days when my math teacher told us about something that goes like this.. "You can never get something from nothing unless that something is nothing too." It seems that this mathematical problems contradicts that statement.. How come we get something from nothing? hehe.. Anyways, I hope you could still give some more solutions to this problem.Get -1 using 0,0,0 I don't believe you can get -1 using ONLY 0's. Using 0's and standard math operations, you can get 0 or 1. If you use other mathematical operations, such as factorial, you can get other numbers like 2 or 6
  • #1
killerinstinct
92
0
Using only three 9's along with elementary math symbols like + or -, see if you can arrange them to represent the number 20. Remeber that 99/9=11.
 
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  • #2
[tex]9+\frac{9}{9}=20_{(base 5)}[/tex]
 
  • #3
Why shouldn't professors solve what even I can solve? [tex]\frac{(9+9)}{.9}=20[/tex]
 
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  • #4
arildno said:
[tex]9+\frac{9}{9}=20_{(base 5)}[/tex]
lol

[tex]9*9 - 9 = 20_{(base 36)}[/tex]

[tex]9*9 + 9 = 20_{(base 45)}[/tex]

[tex]9*(9 + 9) = 20_{(base 81)}[/tex]

[tex]9! + 9 - 9 = 20_{(base 181440)}[/tex]

[tex]9! + 9 + 9 = 20_{(base 181449)}[/tex]

[tex]9^9 - 9 = 20_{(base 193710240)}[/tex]

[tex]9^9 + 9 = 20_{(base 193710249)}[/tex]

etc...
 
  • #5
Bases are not ELEMENTARY MATH!
 
  • #6
killerinstinct said:
Bases are not ELEMENTARY MATH!
I think they are elementary :biggrin:
 
  • #7
Regardless of how "elementary" bases are, the original problem says "the number 20" (which one can reasonably argue to be stated in base 10), instead of "a number with the representation '20' in some base".
 
  • #8
Okay then, I cheated, I'm terribly sorry.
 
  • #9
killerinstinct said:
Bases are not ELEMENTARY MATH!

My textbook called Elementary # Theory has bases in it... :wink:
 
  • #10
( 9² * sqrt(9) ) - sqrt(9) = (81*3)-3 = 240. I choose to use the division symbol / to cross the 4 et voila. :devil:
 
  • #11
In any case, why did you say professor's can't solve this? How many professors did you try?
 
  • #12
I know that there are many complicated (...) solutions to this problem. Many involving bases, but the most simplest solution is given by Grizzlycomet (look above) using only elementary basic math. It is not a matter of "professor not solving the problem", its just a FUN question! Don't interpet me wrong.
 
  • #13
Do you know about the "four fours" variation of this theme?
 
  • #14
Explain questions? (using four 4s to equal something)?
 
  • #15
That's right; if I remember correctly, every number up to and including 12(?) can be written with 4 4's and standard math operations (no silly base shifts..)

I'm not absolutely sure about the last member of this set (i.e., 12), it's been a while since I saw it.

(Of course, lots of other numbers can be written using 4 fours too, but they are not consecutive..)
 
  • #16
1 4x4/(4x4)
2 4x4/(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+4x4/4
9 4+4+4/4
10 (44-4)/4
11 (4!+4)/4+4
12 (4!)x4/(4+4)


I had to use one "44". Is there a way to get 10 without resorting to this?

Njorl
 
  • #17
arildno said:
Okay then, I cheated, I'm terribly sorry.

Very naughty. As punishmnt, you should be whipped with a bundle of rays.
 
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  • #18
Njorl said:
I had to use one "44". Is there a way to get 10 without resorting to this?
Njorl
How about [tex]4+4+\frac{4}{\sqrt{4}}[/tex]
 
  • #20
There's another fun variation on this theme where you line up all the numbers from one to nine in threes and are supposed to make them add up to six by adding only plus, minus, division, multiplication, root and power signs (whole powers and roots, no logs!). You can also use ( and ) (forgot what they're called).

Like this:
Code:
1   1   1 = 6
2   2   2 = 6
3   3   3 = 6
4   4   4 = 6
5   5   5 = 6
6   6   6 = 6
7   7   7 = 6
8   8   8 = 6
9   9   9 = 6

For example (I hope I'm not ruining anything for anyone here :wink:):
6 + 6 - 6 = 6

Have fun.
 
  • #21
Grizzlycomet said:
How about [tex]4+4+\frac{4}{\sqrt{4}}[/tex]

I think using a square root implicity requires a "2".
 
  • #22
professors can't solve this? wow.
 
  • #23
Grizzlycomet said:
How about [tex]4+4+\frac{4}{\sqrt{4}}[/tex]

that works for me
 
  • #24
How about this one?

[(9-sqrt(9))!]/[(sqrt(9)!)^2]

the square root and the square kind of mess it up, but it's still pretty damn sweet
 
  • #25
Sweet. Good work!
 
  • #26
StonedPanda said:
How about this one?

[(9-sqrt(9))!]/[(sqrt(9)!)^2]

the square root and the square kind of mess it up, but it's still pretty damn sweet

That equals 20.

sqrt(9)=3
9-sqrt(9)=6
6!=720

6^2=36

720/36=20

Njorl
 
  • #27
1 1 1 = 6...(1+1+1)!
2 2 2 = 6...2+2+2
3 3 3 = 6...3x3-3
4 4 4 = 6...(4!/4)x40
5 5 5 = 6...5+5/5
6 6 6 = 6...6+6-6
7 7 7 = 6...7-7/7
8 8 8 = 6...(8-81/3)x80
9 9 9 = 6...9-9/(91/2)

Njorl
 
  • #28
How come I never thought of those answers that Njorl did. Hmmm, something is wrong with my brain. lol!
 
  • #29
Njorl said:
1 1 1 = 6...(1+1+1)!
2 2 2 = 6...2+2+2
3 3 3 = 6...3x3-3
4 4 4 = 6...(4!/4)x40
5 5 5 = 6...5+5/5
6 6 6 = 6...6+6-6
7 7 7 = 6...7-7/7
8 8 8 = 6...(8-81/3)x80
9 9 9 = 6...9-9/(91/2)

Njorl

what does 8^0 mean?
what does is equal?

and where do you get 9-9/9^1/2
doesnt 9-9=0, then 0/9^1/2=0?
 
  • #30
x^0 is equal to 1 for all real (and complex) x.

9 - 9/9^(1/2) is interpreted as [tex]9 - \frac{9}{9^{1/2}}[/tex]. If he had meant [tex]\frac{9 - 9}{9^{1/2}}[/tex], he would have written (9 - 9)/9^(1/2). The parantheses are important :P
 
  • #31
How bout this..

Get -1 using 0,0,0 :wink:

Oh and this is mathematically possible without using any tricks..
 
Last edited by a moderator:
  • #32
ExecNight said:
Get -1 using 0,0,0

0 + 0 - 0!

Or to get 6:

(0! + 0! + 0!)!
 
  • #33
[tex]0 - 0^0[/tex]
is this qualified?
 
  • #34
[tex]
-\cos{0} - 0 + 0
[/tex]

and mm...

[tex]
- ( \sin ^2 0 + \cos ^2 0 ) + 0
[/tex]
 
  • #35
futb0l said:
[tex]0 - 0^0[/tex]
is this qualified?
Strictly speaking [itex]0^0[/itex] is not defined. As:

[tex]x^0 = \left( x^1 \right) \left( x^{-1} \right)[/tex]

Therefore:

[tex]x^0 = \frac{x}{x}[/tex]

Which means [itex]x^0 = 1[/itex] when [itex]x \neq 0[/itex]
 
<h2>1. What is the best way to teach elementary math?</h2><p>The best way to teach elementary math is through a combination of hands-on activities, visual aids, and real-life examples. This allows students to engage with the material and understand how it applies to their everyday lives.</p><h2>2. How can I help my child improve their math skills?</h2><p>One of the most effective ways to help your child improve their math skills is to practice regularly with them. This can include playing math games, doing math problems together, and providing real-life examples of how math is used in everyday situations.</p><h2>3. What is the most challenging concept in elementary math?</h2><p>The most challenging concept in elementary math varies from student to student, but some common ones include fractions, long division, and word problems. It is important for teachers and parents to provide extra support and practice for these concepts.</p><h2>4. How can I make math more interesting for my students?</h2><p>One way to make math more interesting for students is to incorporate real-life examples and hands-on activities into the lessons. This can help students see the practical applications of math and make it more engaging for them.</p><h2>5. How can I help my students who struggle with math?</h2><p>To help students who struggle with math, it is important to identify their specific areas of difficulty and provide targeted support and practice. This can include one-on-one instruction, extra practice problems, and visual aids to help students better understand the concepts.</p>

1. What is the best way to teach elementary math?

The best way to teach elementary math is through a combination of hands-on activities, visual aids, and real-life examples. This allows students to engage with the material and understand how it applies to their everyday lives.

2. How can I help my child improve their math skills?

One of the most effective ways to help your child improve their math skills is to practice regularly with them. This can include playing math games, doing math problems together, and providing real-life examples of how math is used in everyday situations.

3. What is the most challenging concept in elementary math?

The most challenging concept in elementary math varies from student to student, but some common ones include fractions, long division, and word problems. It is important for teachers and parents to provide extra support and practice for these concepts.

4. How can I make math more interesting for my students?

One way to make math more interesting for students is to incorporate real-life examples and hands-on activities into the lessons. This can help students see the practical applications of math and make it more engaging for them.

5. How can I help my students who struggle with math?

To help students who struggle with math, it is important to identify their specific areas of difficulty and provide targeted support and practice. This can include one-on-one instruction, extra practice problems, and visual aids to help students better understand the concepts.

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