View unanswered posts | View active topics It is currently Wed Feb 08, 2023 12:12 pm ← Back to the Calcudoku puzzle page Page 1 of 1 [ 10 posts ]
 Print view Previous topic | Next topic
Exponentiation operator
Author Message

Posted on: Sat Sep 24, 2022 12:35 am

Posts: 19
Joined: Wed Jan 05, 2022 8:59 pm The explanation says:

Quote:
Note: this puzzle also uses the exponentiation operator ^
Example: 2^3 = 2 x 2 x 2 = 8
Or, with three digits: 2^4^2 = 2^(4^2) = 2^16 = 65536
Note: evaluation is right to left

What is ment with "Note: evaluation is right to left"?

Does the placement of numbers have effect? When I have 2 boxed horizontal with 625^, does it have to be 54 or can it also be 45?  Posted on: Sat Sep 24, 2022 1:32 pm

Posts: 3181
Joined: Thu May 12, 2011 11:58 pm guidocram wrote:
The explanation says:

Quote:
Note: this puzzle also uses the exponentiation operator ^
Example: 2^3 = 2 x 2 x 2 = 8
Or, with three digits: 2^4^2 = 2^(4^2) = 2^16 = 65536
Note: evaluation is right to left

What is ment with "Note: evaluation is right to left"?

Does the placement of numbers have effect? When I have 2 boxed horizontal with 625^, does it have to be 54 or can it also be 45?

It can be both, the order of the numbers in a cell does not matter (like for any cage and any operator in a Calcudoku).

The note for exponentiation is needed because it matters, take for example 2^4^2:

evaluation left to right:
(2^4)^2 = 16 ^ 2 = 256

evaluation right to left:
2^(4^2) = 2 ^ 16 = 65536

If you assume left to right evaluation, you'll run into cages for which the given result can't be produced
(and I still get messages once in a while about this ) Posted on: Sat Sep 24, 2022 4:18 pm

Posts: 19
Joined: Wed Jan 05, 2022 8:59 pm So when there are 2, 2, and 4 inside the box, it still can be:

4^2^2 = 4^(2^2) = 4^4 = 256
2^4^2 = 2^(4^2) = 2^16 = 65536
2^2^4 = 2^(2^4) = 2^16 = 65536

Correct?  Posted on: Sat Sep 24, 2022 4:49 pm

Posts: 3181
Joined: Thu May 12, 2011 11:58 pm guidocram wrote:
So when there are 2, 2, and 4 inside the box, it still can be:

4^2^2 = 4^(2^2) = 4^4 = 256
2^4^2 = 2^(4^2) = 2^16 = 65536
2^2^4 = 2^(2^4) = 2^16 = 65536

Correct?

yes, all correct  Posted on: Sat Sep 24, 2022 10:29 pm

Posts: 903
Location: Ukraine
Joined: Tue Mar 01, 2016 10:03 pm pnm wrote:
guidocram wrote:
So when there are 2, 2, and 4 inside the box, it still can be:

4^2^2 = 4^(2^2) = 4^4 = 256
2^4^2 = 2^(4^2) = 2^16 = 65536
2^2^4 = 2^(2^4) = 2^16 = 65536

Correct?

yes, all correct Now I’m confused. If either of the above answers is valid, it means that the order of evaluation is irrelevant. What am I missing?  Posted on: Sun Sep 25, 2022 2:59 am

Posts: 19
Joined: Wed Jan 05, 2022 8:59 pm Other way of calculation:

4^2^2 = (4^2)^2 = 16^2 = 256
2^4^2 = (2^4)^2 = 16^2 = 256
2^2^4 = (2^2)^4 = 4^4 = 256

Not a big difference. Though with the current way of calculation it is possible to get 65536 with 2, 2 and 4.

Might be more clear with 2, 3 and 5.  Posted on: Sun Sep 25, 2022 11:06 am

Posts: 3181
Joined: Thu May 12, 2011 11:58 pm paulv66 wrote:
Now I’m confused. If either of the above answers is valid, it means that the order of evaluation is irrelevant.

For 2,2,4, and the result 256, yes. Posted on: Sun Sep 25, 2022 12:29 pm

Posts: 903
Location: Ukraine
Joined: Tue Mar 01, 2016 10:03 pm pnm wrote:
paulv66 wrote:
Now I’m confused. If either of the above answers is valid, it means that the order of evaluation is irrelevant.

For 2,2,4, and the result 256, yes.

So is the order only relevant if there are three different numbers in the cage? Or are you saying that 65,536 is not an acceptable answer for 2,2,4?  Posted on: Sun Sep 25, 2022 12:53 pm

Posts: 3181
Joined: Thu May 12, 2011 11:58 pm paulv66 wrote:
So is the order only relevant if there are three different numbers in the cage? Or are you saying that 65,536 is not an acceptable answer for 2,2,4?

65536 definitely is an acceptable answer, because the evaluation order is right-to-left.

And as with cages with 3 cells or more with subtraction/division,
there exists an ordering for which the result is produced.

edit: here I'm assuming that when you write "order", you mean the ordering of evaluation?
(not the ordering of the numbers)

(this is maybe a cause of confusion) Posted on: Sun Sep 25, 2022 1:33 pm

Posts: 903
Location: Ukraine
Joined: Tue Mar 01, 2016 10:03 pm pnm wrote:
paulv66 wrote:
So is the order only relevant if there are three different numbers in the cage? Or are you saying that 65,536 is not an acceptable answer for 2,2,4?

65536 definitely is an acceptable answer, because the evaluation order is right-to-left.

And as with cages with 3 cells or more with subtraction/division,
there exists an ordering for which the result is produced.

edit: here I'm assuming that when you write "order", you mean the ordering of evaluation?
(not the ordering of the numbers)

(this is maybe a cause of confusion)

Thanks Patrick.

My confusion was caused by the fact that I was assuming that the evaluation order was left to right, in which case the only acceptable answer would be 256. I’ve no idea why I made that assumption when the instructions clearly say right to left. I can only assume that it’s because I often struggle to distinguish left from right and find myself having to correct what I say when I’m giving directions. Display posts from previous:  Sort by Page 1 of 1 [ 10 posts ]

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ English    Announcements    Calcudoku General    Other number stuff    Solving strategies and tips    Specific puzzles / your own puzzles (Calcudoku / Killer Sudoku)    Timed Puzzles    Bugs and errors    Killer Sudoku    Sudoku solving / your own Sudokus / your own other puzzles Nederlands    Aankondigingen    Calcudoku Algemeen    Oplostips en strategieën Italiano    Calcudoku Generale    Strategie e consigli per risolvere Español    Avisos    Calcudoku - General    Estrategias de solución y aspectos relevantes
All forum contents © Patrick Min, and by the post authors.

Forum software phpBB © 2000, 2002, 2005, 2007 phpBB Group.
Designed by STSoftware.