Calculator

**fundu** · Dec 17th, 2003, 06:09 PM

This is a slightly more interesting problem featuring calculators.

What is the minimum number of mathematical operations needed (buttons pressed), if we want to get all the numbers from 0 to 10? Use a scientific calculator and anytime you cannot press any digit button. I mean we can only use buttons on the top (like log, triginometric, etc).

Definitely it will start from Zero as most scientific calculators do that already.

A simple example being just take log inverse twice. The 1st one will give 1 and the 2nd will give 10.

Also it would be further interesting to find the desired count if we add the restriction that one should not arrive to the same number more than once.

TRY!!!!!!!!!

**Acidic** · Dec 17th, 2003, 06:25 PM

ok type 0
now it starts
e^x that gets you numeber 1
+ans gets you 2, then 4,then 8
then I can go back and get 10
can't get any others, yet.

**Acidic** · Dec 17th, 2003, 06:37 PM

I get 1 through to 10 in 19 moves (excluding the zero at the start).

method:
[zero]
[2nd] [10^x] [2nd] [ans] [=]
[->] [X] [=]
[+] [X] [=]
[=]
[=]
[=]
[=]
[=]
[=]
[=]
[=]

There, 19 moves on a TI-83, or was I cheating?

**kedaman** · Dec 17th, 2003, 06:44 PM

2: !+!
3: !+!+!
4: !+!*ANS
5: !+!*ANS+!
6: !+!*ANS+!+!
7 loginv loginv-!-!-!
8 loginv loginv-!-!
9 loginv loginv-!
yeah I know i'm lazy, but i'm also tired and have to get some sleep..

**alkatran** · Dec 17th, 2003, 10:01 PM

Does it count if we get an answer that is actually a loop?

For example, if we solve sin(x*whatevertoget1) = 0

**kedaman** · Dec 18th, 2003, 12:35 AM

minor improvement
4: !+! ^2
5: !+! ^2+!
6: !+! ^2+!+!

**NoteMe** · Dec 18th, 2003, 09:32 AM

How many are the smallest amount of number you are actually up to now....

I only have to push 13 times....

**fundu** · Dec 18th, 2003, 01:05 PM

Hey! What is this? Don't use any programmable calculator. When I said standard scientific calculator, I meant we can use the following buttons only:
1. The three Trigonometric functions (sin, cos, tan) and their inverse (use only degrees. No radians)
2. Logarithmic function (Ln, log, e^x) and their inverse
3. Factorial function (!)
4. 1/x
5. Powers & Roots (x^2, x^3, x^(1/2), x^(1/3)) only, no usage of the x^y as U cannot use memory and even can't press a digit

No addition, substraction, multiplication, division and memory usage. If U press = its not considered a count. By the way I asked for minimum mathematical operations, not buttons pressed.

For examples:
Start with 0.
1. Do !, get 1.
2. Do Log Inverse, get 10.
3. Do x^2, get 100
4. Do Log, get 2
5. Do x^2, get 4
6. Do x^(1/2), get 2
7. Do x^3, get 8
8. Do x^(1/3), get 2
9. Do Log Inverse, get 100
10. Do x^(1/2), get 10
11. Do Log Inverse, get 10^10
12. Do x^(1/2), get 10^5
13. Do Log, get 5

This was just a redundant example to produce some numbers. Still 3, 6, 7 and 9 are left. Moreover there are methods to get these 7 numbers (which I showed), in less than 13 operations. Notice that throughout these steps, I never pressed the = button.

Remember: Don't use memory.

Enjoy!

**NoteMe** · Dec 18th, 2003, 01:08 PM

BTW...arey you allowed to use + - / *????

**fundu** · Dec 18th, 2003, 01:24 PM

As I said U cannot use +, -, *, /

Remember the old scientific calculators where these buttons used to be with the number buttons on the lower half. We can only use the upper half.

**NoteMe** · Dec 18th, 2003, 02:27 PM

But you said that we could use X^2 and that is a number....2 has to be pressed....or did I missunderstand that too?

**fundu** · Dec 18th, 2003, 02:41 PM

There is a button in scientific calculators that says X^2 and x^(1/2). It just returns the x^2 of the number on the screen if you press the button. If U want the other use shift of inv button before pressing this one.

If U don't have a square button, U can use x^y where U can press 2. But remember use only 2, 3, 1/2 and 1/3 as powers.

**DiGiTaIErRoR** · Dec 18th, 2003, 03:43 PM

Ok...

0! = 1
int(Tan(ans)^2) = 2
abs(int(tan(ans))) = 3
abs(int(tan(ans^3))) = 4
int(tan(ln(ans))) = 5
abs(int(tan(ans^(1/3))) = 8
abs(int(tan(ans))) = 7
int(e^(ans^(1/3))) = 6
int(e^ans^(1/2)) = 11
int(e^ans^(1/3)) = 9
0! = 1, inverse log(ans) = 10

Good?

**fundu** · Dec 18th, 2003, 04:22 PM

I wrote that use only degrees in trigonometric functions. Don't use radians.

**fundu** · Dec 18th, 2003, 04:24 PM

Also use of int() & abs() is not permitted. The only permitted functions are the one I told earlier.

I think the toughest is to get 7.

**DiGiTaIErRoR** · Dec 18th, 2003, 04:37 PM

Originally posted by fundu
Also use of int() & abs() is not permitted. The only permitted functions are the one I told earlier.

I think the toughest is to get 7.

Anal retentive bastard.

**NoteMe** · Dec 18th, 2003, 04:38 PM

Originally posted by DiGiTaIErRoR

When I get more time to waste I'll try it without addition.

If you could use addition. You could just write

e0

then

Ans + e0

then

enter
enter
enter
enter

and so on....

and you would have 1,2,3,4,5,and so on...

**DiGiTaIErRoR** · Dec 18th, 2003, 04:39 PM

Originally posted by NoteMe
If you could use addition. You could just write

e0

then

Ans + e0

then

enter
enter
enter
enter

and so on....

and you would have 1,2,3,4,5,and so on...

But that's not creative!

**NoteMe** · Dec 18th, 2003, 04:40 PM

Originally posted by DiGiTaIErRoR
But that's not creative!

You don't have to be creative to have the best solution.....

**kedaman** · Dec 18th, 2003, 04:40 PM

I can get everything except 7 atm

**DiGiTaIErRoR** · Dec 18th, 2003, 04:41 PM

Originally posted by fundu
I wrote that use only degrees in trigonometric functions. Don't use radians.

Psh, Screw degrees. Radians own you! 2pi radians, to be exact.

**DiGiTaIErRoR** · Dec 18th, 2003, 04:42 PM

Originally posted by NoteMe
You don't have to be creative to have the best solution.....

Best solution? What happened to good ol' mathematic fun?

**NoteMe** · Dec 18th, 2003, 04:44 PM

Originally posted by DiGiTaIErRoR
Best solution? What happened to good ol' mathematic fun?

What about it....I think it was fun finding out that I could do it in only 5 button presses....

**fundu** · Dec 18th, 2003, 04:44 PM

If U all want I may post one method of getting 7?

**kedaman** · Dec 18th, 2003, 04:53 PM

veto! I've been trying to work something out for ages.. you can't just do that

**fundu** · Dec 19th, 2003, 05:42 PM

One way to get 7 is:

1. I am starting from 8
2. Take sin of 8
3. Now take cos inverse, It will return 82
4. Take log inverse, get 10^82
5. Take root, get 10^41
6. Take log, get 41
7. Take sin of 41
8. Now do cos inverse, get 49
9. Take root, get 7 !!!!!!!

Howz that?

I think 3 was pretty simple so didn't wrote that.

If U don't know then in short U can start from 5, do 5!, get 120 take tan of 120 & square it to get 3. Go on 2 get 6 & 9.

Though still better methods are yet 2 come from U studds.

If on one is interested & I receive no replies, then I will close the thread on monday.

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