aaargh

[ctrlaltdel]

ok, ive had enuff, this one has been driving me nuts for so long ive given up...

the whole thing is to use numerals 2,2,9, and 9 and the following operations:
+
-
*
/
!
sqrt
^
( )

to write expressions equal to each number from 0 to 132 inclusive. all easy enough, so why am i stuck on 94???

can you help out - use two 2s and two 9s to express 94...

[UnheardVoice]

Questions:
With the sqrt operation, it doesn't "use up" one of the twos?
And can I combine the twos and nines together to make larger numbers like 92, 29, 99, and 22?
And do I have infinite amount of each operation?

If YES to all, then:

94 = (92 + 2)^(sqrt sqrt sqrt sqrt sqrt sqrt... [infinite] of 9)
= (94)^(1)
= 94

But I could be wrong.

[ctrlaltdel]

yes to all except the infinite number of operations, sorry...

[miketrig]

This is how I got 94:

94=99-sqrt(9)-2

[Chuck]

That uses three nines and only one two. I thought two of each were required.

[This message has been edited by Chuck (edited 01-29-2002 10:51 AM).]

[ctrlaltdel]

you can ONLY and at the same time you MUST use both 2s and both 9s.

using three of one and one of the other is not acceptable

[hey_herb]

How about

9^2 + 9 + 2 + 2 = 94

or is using a square considered using a 2.

[ctrlaltdel]

well did you use it or not?

you could use 9x9 instead, which would rob you of that extra 9 which you need later... thats the whole puzzle - to use the four numerals only and all of them

[Icarus]

I hope I remember my math.

9!, if I remember correctly is 9+8+7+6+5+4+3+2+1=45, right ?

So how about 9!*2 + (9/2)

You get 94.5, but you simply drop the decimal ?

[Icarus]

I hope I remember my math.

9!, if I remember correctly is 9+8+7+6+5+4+3+2+1=45, right ?

So how about 9!*2 + (9/2)

You get 94.5, but you simply drop the decimal ?

[Quailman]

9! = 9*8*7*6*5*4*3*2*1 = 362,880

[ctrlaltdel]

oh no, you dont simply drop the decimal, and please ppl, i have given some time to the puzzle so dont give me answers with 3 digits of one kind or however else twisting the rules... i think the rules are clear enough.

and as pointed out, factorial is got by mulitplying all the integers down to 0, excluding 0.

the most "tricky" (geeez) part of the rules is that you can use sqrt wiht OR without losing a 2.

[Quailman]

I know we can't drop the decimal, but can we add one? For example, 9/.2 = 45

[Ghost Post]

nah i dont think the king(who i cant even think of a name for)would like that because
1 you have to use all of the numbers(silly)
2 .2=0.2 not 2(thats what you call brain science)

believe me, there is no easy solution to this lark, using numbers to find answers is one of my strong points, the only solution i thought of was using the same method as richard, BAH...

[This message has been edited by johnny4444 (edited 01-29-2002 04:06 PM).]

[ctrlaltdel]

i got to the point where i started toying with the idea that a totally crazy loop of going into stupidly big values and dropping back would give me the 94, but idk...

thinking of something like... oh... sqrt(9)^92! - 2 ... or blahblahblah and then just take the right number of square roots off of that... but thats just hitting for one number in a gazillion...

[richardb]

Noting that (sqrt(9))! = 6,

94 = 92 + sqrt((sqrt(9))!-2)

[HappyMutant]

*applause*

[ctrlaltdel]

DUH.... stupid me.... thnx a lot richard!!! gr8 work!

so ok, now im SURE... all integers 0... 132 inclusive can be expressed in similar ways using two 2s and two 9s. i think 107 was a tricky one too...

if you guys want to go on through all of them i wont stop you, if you dont care about the rest of them i consider this thread killed...

[Ghost Post]

excelent, now by rule of hamtofry, gives richard a frog(if he joins)

[Chuck]

We could start again with 133.

[ctrlaltdel]

ok lets see how far we can get... i tried a few things on 133 but i can only get three 2s and two 9s so far...