# A lot of 9.

kbaumen
Posers and Puzzles 08 Mar '08 19:25
1. 08 Mar '08 19:252 edits
I was just watching a local adoption of the show "Are you smarter than a 5thgrader?" and there was an old lady playing. She struggled to answer a question "Find a way to express 10 with five 9". While she figured out 99/ 9 - 9/9 = 10, I figured out 14 more ways to do it?

How many ways can you guys find?

P.s. I used derivatives, trigonometry, logarithms. There definitely are more ways, but the number I gave is how many I found during the question.
2. 08 Mar '08 19:471 edit
Originally posted by kbaumen
I was just watching a local adoption of the show "Are you smarter than a 5thgrader?" and there was an old lady playing. She struggled to answer a question "Find a way to express 10 with five 9". While she figured out (99 - 9) - 9/9 = 10, I figured out 14 more ways to do it?

How many ways can you guys find?

P.s. I used derivatives, trigonometry, logarit ...[text shortened]... ere definitely are more ways, but the number I gave is how many I found during the question.
the old lady lost didn't she?
Because she found a way to express 89 inted of 10:
(99-9)-9/9=90-1=89 !!!
here's a easy one : 99/99 + 9
3. 08 Mar '08 19:55
Originally posted by alexdino
the old lady lost didn't she?
Because she found a way to express 89 inted of 10:
(99-9)-9/9=90-1=89 !!!
here's a easy one : 99/99 + 9
Ooops, sorry, my mistake. Fixed now.
4. 08 Mar '08 20:50
some easy ones off the top of my head:

1. 9-9+9+(9/9)
2.(9/9)^99 + 9
3. 9-9+9+log(9-9)
4. 9-9+9+[log(base 9) of 9]
5. 9/9+[9th root of 9^9)

etc. if you allow the use of log base 9, 9th power and 9th root to achieve a value of 1, you can find tons and tons

i wonder how well 5 9s could be used to write the set of whole numbers, a la the classic four 4s problem? intriguing..
5. 08 Mar '08 21:191 edit
I'll post some others I found:

sin9sin9 + cos9cos9 + 9 = 10
(99 - 9)/9 + derivative(9) = 10 (I suppose if you derive a constant function, hence a constant number, the derivative is 0)
(tg9ctg9 + 9) * 9 / 9 = 10

Eh, yeah, there really are tons of possibilities.

Ok, let's make 1 to 100 with five 9. (with only + - * /, hence no trigonometry, logarithmic expressions, calculus, combinatorics and other creepy stuff)

I'll start:

1 = (99 - 9) / 9 - 9
6. 08 Mar '08 21:301 edit
2 = 9/9+(9/9)^9
3 = (9+9)/9 + 9/9
7. 08 Mar '08 21:35
4 = (9+9+9+9)/9
8. 08 Mar '08 21:532 edits
5 = sqrt(9) + 9/9 + 9/9

EDIT: Damn, I didn't mention square root. Ah, consider it an option. I think some numbers will be quite hard to get without sqrt. However, no sqr(9), hence 9^2, please.
9. 09 Mar '08 00:10
6 = (9/9)^9 * (9 - sqrt(9))
numbers not so close to multiples of 9 are a bit more dificult so i thinc that without sqrt you can't get them wiith only 5 9s.
but you can always try!
7 = 9 - 9/9- 9/9
10. 09 Mar '08 06:19
8 = 9-9+9-9/9
11. 09 Mar '08 06:35
9 = (9*9)-(9*9) + 9
12. 09 Mar '08 09:29
As already posted 10 = 99/99 + 9

11 = 9 + 9/9 + 9/9
13. 09 Mar '08 15:13
12 = (9+9+9)/9 + 9
13 = 9 + sqrt(9) + (9+9)/9
14 = 9 +9 - sqrt(9) - 9/9
15 = (9 - sqrt(9) + 9) * 9/9
14. 09 Mar '08 16:512 edits
Originally posted by alexdino

13 = 9 + sqrt(9) + (9+9)/9
Check this one (above) again.

16 = 9 + 9 - sqrt(9) + 9/9
15. 09 Mar '08 17:40
ooopps
13 = 9 + sqrt(9) + (9/9)^9