Elementary math that professors cant solve

1. May 27, 2004

killerinstinct

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.

2. May 27, 2004

arildno

$$9+\frac{9}{9}=20_{(base 5)}$$

3. May 27, 2004

Grizzlycomet

Why shouldnt professors solve what even I can solve? $$\frac{(9+9)}{.9}=20$$

Last edited: May 28, 2004
4. May 27, 2004

Zurtex

lol

$$9*9 - 9 = 20_{(base 36)}$$

$$9*9 + 9 = 20_{(base 45)}$$

$$9*(9 + 9) = 20_{(base 81)}$$

$$9! + 9 - 9 = 20_{(base 181440)}$$

$$9! + 9 + 9 = 20_{(base 181449)}$$

$$9^9 - 9 = 20_{(base 193710240)}$$

$$9^9 + 9 = 20_{(base 193710249)}$$

etc...

5. May 27, 2004

killerinstinct

Bases are not ELEMENTARY MATH!!!

6. May 27, 2004

arildno

I think they are elementary

7. May 27, 2004

ahrkron

Staff Emeritus
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. May 27, 2004

arildno

Okay then, I cheated, I'm terribly sorry.

9. May 27, 2004

fourier jr

My textbook called Elementary # Theory has bases in it....

10. May 28, 2004

Simon666

( 9² * sqrt(9) ) - sqrt(9) = (81*3)-3 = 240. I choose to use the division symbol / to cross the 4 et voila.

11. May 28, 2004

HallsofIvy

Staff Emeritus
In any case, why did you say professor's can't solve this? How many professors did you try?

12. May 28, 2004

killerinstinct

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. May 28, 2004

arildno

Do you know about the "four fours" variation of this theme?

14. May 28, 2004

killerinstinct

Explain questions? (using four 4s to equal something)?

15. May 28, 2004

arildno

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. May 28, 2004

Njorl

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. May 28, 2004

Bob3141592

Very naughty. As punishmnt, you should be whipped with a bundle of rays.

Last edited: May 28, 2004
18. May 28, 2004

Grizzlycomet

How about $$4+4+\frac{4}{\sqrt{4}}$$

19. May 29, 2004

Euphoriet

20. May 30, 2004

Gunni

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 (Text):

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 ):
6 + 6 - 6 = 6

Have fun.