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 April 2 7x7 Difficult (possible very minor spoiler) 
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Posted on: Mon Apr 02, 2012 6:04 am




Posts: 78
Joined: Sun Mar 04, 2012 3:43 am
Post April 2 7x7 Difficult (possible very minor spoiler)
I am working this puzzle with continuous error checking on, and doing the 3-cell cage 262144^.

The prime factorization of 262144 is 2^18.

One possible way to complete this cage should be [2,3,6], since (2^3)^6 = 8^6 = 262144. However, the cage label turns red with these three numbers.

The cage label is black when [2,3,4] is entered, since 4^(3^2) = 4^9 = 262144 as well. But shouldn't both work?

Is the problem here the note for the exponentiation operator at the bottom, "evaluation is right to left"? In other words, do the right-most exponentiation first, and work backwards?


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Posted on: Mon Apr 02, 2012 6:09 am




Posts: 175
Joined: Fri May 13, 2011 2:11 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
jake4 wrote:
I am working this puzzle with continuous error checking on, and doing the 3-cell cage 262144^.

The prime factorization of 262144 is 2^18.

One possible way to complete this cage should be [2,3,6], since (2^3)^6 = 8^6 = 262144. However, the cage label turns red with these three numbers.

The cage label is black when [2,3,4] is entered, since 4^(3^2) = 4^9 = 262144 as well. But shouldn't both work?

Is the problem here the note for the exponentiation operator at the bottom, "evaluation is right to left"? In other words, do the right-most exponentiation first, and work backwards?

Right to left means with 2^3^6, you do 3^6, and then do 2^729.

The right to left things explain the reason it is as it is.


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Posted on: Mon Apr 02, 2012 6:27 am




Posts: 78
Joined: Sun Mar 04, 2012 3:43 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
starling wrote:
The right to left things explain the reason it is as it is.

Well, not really. It explains what it is, not why it is. I think I've got the "what it is" part now, it just took me a little while to work it out.

So, why is it this way? Is it supposed to make the puzzle easier to solve? Or is it based on the way Patrick creates the puzzle?


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Posted on: Mon Apr 02, 2012 8:21 am




Posts: 175
Joined: Fri May 13, 2011 2:11 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
jake4 wrote:
starling wrote:
The right to left things explain the reason it is as it is.

Well, not really. It explains what it is, not why it is. I think I've got the "what it is" part now, it just took me a little while to work it out.

So, why is it this way? Is it supposed to make the puzzle easier to solve? Or is it based on the way Patrick creates the puzzle?

Oh, you're looking for a mathematical reason why it's that way?

That's the way order of operation works for nested exponents, and that's the only way I really know how to explain it.


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Posted on: Mon Apr 02, 2012 10:45 am




Posts: 2194
Joined: Thu May 12, 2011 11:58 pm
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
jake4 wrote:
starling wrote:
The right to left things explain the reason it is as it is.

Well, not really. It explains what it is, not why it is. I think I've got the "what it is" part now, it just took me a little while to work it out.

So, why is it this way? Is it supposed to make the puzzle easier to solve? Or is it based on the way Patrick creates the puzzle?

Yes, I suppose. When I first added the puzzle with exponentiation,
the evaluation order was left to right. Then someone pointed out
that for exponentiation with more than 2 numbers, the convention
is to evaluate from right to left (of course), so then I changed it.

Patrick


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Posted on: Mon Apr 02, 2012 10:59 am




Posts: 490
Location: Ladysmith, BC, Canada
Joined: Fri May 13, 2011 1:37 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
I am wondering whether or not one should be discussing a puzzle whose due date is not up yet......in the past, this type of topic was only posted after the expiry date had occurred......not that it matters to me.....but just a thought.


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Posted on: Mon Apr 02, 2012 11:23 am




Posts: 2194
Joined: Thu May 12, 2011 11:58 pm
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
beaker wrote:
I am wondering whether or not one should be discussing a puzzle whose due date is not up yet......in the past, this type of topic was only posted after the expiry date had occurred......not that it matters to me.....but just a thought.

Well in this case there was only a tiny bit of info about one cage,
_and_ the subject even warned "possible very minor spoiler" ...


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Posted on: Mon Apr 02, 2012 1:59 pm




Posts: 175
Joined: Fri May 13, 2011 2:11 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
pnm wrote:
beaker wrote:
I am wondering whether or not one should be discussing a puzzle whose due date is not up yet......in the past, this type of topic was only posted after the expiry date had occurred......not that it matters to me.....but just a thought.

Well in this case there was only a tiny bit of info about one cage,
_and_ the subject even warned "possible very minor spoiler" ...

And it was a cage whose value took 3 steps to deduce, so it's not like you would have gotten much help from that.


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Posted on: Tue Apr 03, 2012 4:13 am




Posts: 78
Joined: Sun Mar 04, 2012 3:43 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
pnm wrote:
jake4 wrote:
starling wrote:
The right to left things explain the reason it is as it is.

Well, not really. It explains what it is, not why it is. I think I've got the "what it is" part now, it just took me a little while to work it out.

So, why is it this way? Is it supposed to make the puzzle easier to solve? Or is it based on the way Patrick creates the puzzle?

Yes, I suppose. When I first added the puzzle with exponentiation,
the evaluation order was left to right. Then someone pointed out
that for exponentiation with more than 2 numbers, the convention
is to evaluate from right to left (of course), so then I changed it.

Patrick

Well, there you go; that is an EXCELLENT reason to do it that way! :) I guess I just assumed I could add parentheses where I wanted to.

Thanks all!


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Posted on: Tue Apr 03, 2012 2:52 pm




Posts: 116
Joined: Sat May 14, 2011 3:18 am
Post Re: April 2 7x7 Difficult (possible very minor spoiler)
On this particular puzzle, it was easier by far for me to look at the 18+ cage and realize that the only way to get to 18 was with 5,6,7, given that I had already determined that 1,8 was the only viable combination for the 9+ cage. That left 2,3,4 for the huge exponent. So I just put those numbers in and was relieved when the cage stayed black! :-)


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