What's the largest total you can find...
 C
 Robust
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What's the largest total you can find...
...using the digits 1,2,3 and 4 and any operation(s) you want?
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Colin Occupants wrote:"Ooof! Tubs! etc"
 Rorschach
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 Joined: 02 Jun 2008, 12:43
Re: What's the largest total you can find...
4 to the power 231
Too big for my calculator!
Too big for my calculator!
Bugger off.
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
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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Colin Occupants wrote:"Ooof! Tubs! etc"
 Rorschach
 Posts: 2247
 Joined: 02 Jun 2008, 12:43
Re: What's the largest total you can find...
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.
 Robert
 Posts: 1254
 Joined: 27 Dec 2013, 13:24
Re: What's the largest total you can find...
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.
 Robert
 Posts: 1254
 Joined: 27 Dec 2013, 13:24
Re: What's the largest total you can find...
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.
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
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 321C 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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Colin Occupants wrote:"Ooof! Tubs! etc"
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
Robert wrote:There is no bigger sum possible with these numbers.
Maybe
Maybe not
How good is your combinations and permutations...?
!......
Colin Occupants wrote:"Ooof! Tubs! etc"
 Robert
 Posts: 1254
 Joined: 27 Dec 2013, 13:24
Re: What's the largest total you can find...
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

 Posts: 1120
 Joined: 05 Jul 2017, 23:05
Re: What's the largest total you can find...
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

 Posts: 1120
 Joined: 05 Jul 2017, 23:05
Re: What's the largest total you can find...
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.
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
What about 4321!....?
[4321 factorial]
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[4321 factorial]
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Colin Occupants wrote:"Ooof! Tubs! etc"
 soundchaser
 Rokster & Rollster
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Re: What's the largest total you can find...
There used to be a Total garage near me. That was pretty large.

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 Joined: 05 Jul 2017, 23:05
Re: What's the largest total you can find...
C wrote:What about 4321!....?
[4321 factorial]
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Well, what about it?
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
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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Colin Occupants wrote:"Ooof! Tubs! etc"
 Robert
 Posts: 1254
 Joined: 27 Dec 2013, 13:24
Re: What's the largest total you can find...
C wrote:Positive Passion wrote:C wrote:What about 4321!....?
[4321 factorial]
.
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.
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
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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Colin Occupants wrote:"Ooof! Tubs! etc"
 Rorschach
 Posts: 2247
 Joined: 02 Jun 2008, 12:43
Re: What's the largest total you can find...
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.
 Robert
 Posts: 1254
 Joined: 27 Dec 2013, 13:24
Re: What's the largest total you can find...
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?
.
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.
 C
 Robust
 Posts: 55507
 Joined: 22 Jul 2003, 19:06
Re: What's the largest total you can find...
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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Colin Occupants wrote:"Ooof! Tubs! etc"