What's the largest total you can find...

in reality, all of this has been a total load of old bollocks
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C
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What's the largest total you can find...

Postby C » 09 Mar 2020, 14:19

...using the digits 1,2,3 and 4 and any operation(s) you want?




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Re: What's the largest total you can find...

Postby Rorschach » 09 Mar 2020, 15:20

4 to the power 231

Too big for my calculator!
Bugger off.

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Re: What's the largest total you can find...

Postby C » 09 Mar 2020, 15:33

Rorschach wrote:4 to the power 231

Too big for my calculator!


Very good thinking, but

4 to the power 321 would be larger.

Wouldn't it?

What about 42 to the power 31 is that larger or smaller I wonder?

Or 31 to the power 42.

Which of these two gives the largest value and are they larger than our first attempts?

Is there anything larger than any of that stuff?





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Re: What's the largest total you can find...

Postby Rorschach » 09 Mar 2020, 16:00

C wrote:
Rorschach wrote:4 to the power 231

Too big for my calculator!


Very good thinking, but

4 to the power 321 would be larger.

Wouldn't it?


Doh! Mistype! Of course I meant 321

C wrote:What about 42 to the power 31 is that larger or smaller I wonder?

Or 31 to the power 42.

Which of these two gives the largest value and are they larger than our first attempts?


I imagine 4 to the power 321 would be much larger than either of those but I don't know for sure.

C wrote:Is there anything larger than any of that stuff?


Maybe using some notation I'm not familiar with but my maths knowledge is pretty basic.
Bugger off.

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Robert
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Re: What's the largest total you can find...

Postby Robert » 09 Mar 2020, 16:11

C wrote:
Rorschach wrote:4 to the power 231

Too big for my calculator!


Very good thinking, but

4 to the power 321 would be larger.

Wouldn't it?

What about 42 to the power 31 is that larger or smaller I wonder?

Or 31 to the power 42.

Which of these two gives the largest value and are they larger than our first attempts?

Is there anything larger than any of that stuff?





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4 to the power of 321 is by far the largest of these. It's easy to see that the other option ( 42 ttpo 31) is much lower. To reach 42 you need 4 to the power of less than 3 only. so basically you're then still left with 42 ttpo 318. There is no bigger sum possible with these numbers.

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Re: What's the largest total you can find...

Postby Robert » 09 Mar 2020, 16:14

Robert wrote:
C wrote:
Rorschach wrote:4 to the power 231

Too big for my calculator!


Very good thinking, but

4 to the power 321 would be larger.

Wouldn't it?

What about 42 to the power 31 is that larger or smaller I wonder?

Or 31 to the power 42.

Which of these two gives the largest value and are they larger than our first attempts?

Is there anything larger than any of that stuff?





.


4 to the power of 321 is by far the largest of these. It's easy to see that the other option ( 42 ttpo 31) is much lower. To reach 42 you need 4 to the power of less than 3 only. so basically you're then still left with 42 ttpo 318. There is no bigger sum possible with these numbers.


BTW, you can easily calculate this in excel. Use the formula: =4^321 and you will see the total won't even fit on your screen.

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Re: What's the largest total you can find...

Postby C » 09 Mar 2020, 17:18

Rorschach wrote:
C wrote:
Rorschach wrote:4 to the power 231

Too big for my calculator!


Very good thinking, but

4 to the power 321 would be larger.

Wouldn't it?


Doh! Mistype! Of course I meant 321

C wrote:What about 42 to the power 31 is that larger or smaller I wonder?

Or 31 to the power 42.

Which of these two gives the largest value and are they larger than our first attempts?


I imagine 4 to the power 321 would be much larger than either of those but I don't know for sure.

C wrote:Is there anything larger than any of that stuff?


Maybe using some notation I'm not familiar with but my maths knowledge is pretty basic.


You've done very well!




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Re: What's the largest total you can find...

Postby C » 09 Mar 2020, 17:22

Robert wrote:There is no bigger sum possible with these numbers.


Maybe

Maybe not

How good is your combinations and permutations...?






!......
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Re: What's the largest total you can find...

Postby Robert » 09 Mar 2020, 19:42

C wrote:
Robert wrote:There is no bigger sum possible with these numbers.


Maybe

Maybe not

How good is your combinations and permutations...?






!......


Am starting to think the answer is probably 3 ttpo 421

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Re: What's the largest total you can find...

Postby Positive Passion » 09 Mar 2020, 19:45

Robert wrote:
C wrote:
Robert wrote:There is no bigger sum possible with these numbers.


Maybe

Maybe not

How good is your combinations and permutations...?






!......


Am starting to think the answer is probably 3 ttpo 421

Surely 2 ttpo 431

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Re: What's the largest total you can find...

Postby Positive Passion » 09 Mar 2020, 20:21

Positive Passion wrote:
Robert wrote:
C wrote:
Maybe

Maybe not

How good is your combinations and permutations...?






!......


Am starting to think the answer is probably 3 ttpo 421

Surely 2 ttpo 431


No I think 3 ttpo 421 is bigger.

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Re: What's the largest total you can find...

Postby C » 10 Mar 2020, 15:06

What about 4321!....?

[4321 factorial]





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Re: What's the largest total you can find...

Postby soundchaser » 10 Mar 2020, 16:38

There used to be a Total garage near me. That was pretty large.

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Re: What's the largest total you can find...

Postby Positive Passion » 10 Mar 2020, 19:29

C wrote:What about 4321!....?

[4321 factorial]





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Well, what about it?

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Re: What's the largest total you can find...

Postby C » 10 Mar 2020, 19:45

Positive Passion wrote:
C wrote:What about 4321!....?

[4321 factorial]





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Well, what about it?


The largest value (?)

4321 x 4320 x 4319 x 4318 x 4317 x....x 3 x 2 x 1





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Re: What's the largest total you can find...

Postby Robert » 10 Mar 2020, 21:36

C wrote:
Positive Passion wrote:
C wrote:What about 4321!....?

[4321 factorial]





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Well, what about it?


The largest value (?)

4321 x 4320 x 4319 x 4318 x 4317 x....x 3 x 2 x 1





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I was going on the assumption that each digit could only be used once.

Besides, you did not give 0, 5,6,7,8 and nine as options.

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Re: What's the largest total you can find...

Postby C » 10 Mar 2020, 22:40

Robert wrote:
I was going on the assumption that each digit could only be used once.

Besides, you did not give 0, 5,6,7,8 and nine as options.


I have only used the four digits 1,2,3 and 4 with the factorial sign ' ! '

In any of the calculations we will use other digits

Also, for example, 34 to the power 12 uses 3 and 4 twelve times

34 x 34 x 34 x ...

and when you calculate the answer other digits will be included

Do you agree?





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Re: What's the largest total you can find...

Postby Rorschach » 11 Mar 2020, 09:01

C wrote:
and when you calculate the answer other digits will be included

Do you agree?


That's how I understood it. In fact I was wondering about factorials (do they still refer to the symbol as 'bang'?) but couldn't remember how they worked.
Bugger off.

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Re: What's the largest total you can find...

Postby Robert » 11 Mar 2020, 13:50

C wrote:
Robert wrote:
I was going on the assumption that each digit could only be used once.

Besides, you did not give 0, 5,6,7,8 and nine as options.


I have only used the four digits 1,2,3 and 4 with the factorial sign ' ! '

In any of the calculations we will use other digits

Also, for example, 34 to the power 12 uses 3 and 4 twelve times

34 x 34 x 34 x ...

and when you calculate the answer other digits will be included

Do you agree?





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No I don't agree. Surely the results of calculations will include other digits but in the case of 3 ttpo 421 only 4,3,2 and 1 are used. When you just write it out, only 3 and 421 are used ( although the result obviously includes other digits).

In the case of a faculty, written out as you did 4321 x 4320 x 4319 etc etc, you are obviously using other digits.

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Re: What's the largest total you can find...

Postby C » 11 Mar 2020, 15:10

Robert wrote:In the case of a faculty, written out as you did 4321 x 4320 x 4319 etc etc, you are obviously using other digits.


A fair point.

That's the great thing about the creativity of mathematics.

We disagree but that's okay.

I will argue that 4321! is a reasonable interpretation particularly as I did not say or take your interpretation

For example

? + $ = 5

Therefore ? = $ = 2.5 is one solution

I didn't say ? and $ were different and I didn't say the values were whole numbers.

If I don't say - anything (mathematically sound) goes

My view is that my solution addresses the question

What you reckon?




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