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Right to left exponentiation
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Posted on: Mon Jan 19, 2015 1:30 pm

Posts: 188
Joined: Thu May 12, 2011 11:51 pm
Right to left exponentiation
In today's 7x7 difficult puzzle I did not understand why (2 ^ 2) ^ 5 was not a valid answer for 1024. Patrick tells me that it violates the right to left convention. I'm not sure that I understand that, but at least the autocorrect will tell me when I'm in the wrong zone.

Posted on: Mon Jan 19, 2015 2:54 pm

Posts: 2333
Joined: Thu May 12, 2011 11:58 pm
Re: Right to left exponentiation
This issue pops up every once in a while, see for example:

viewtopic.php?f=16&t=183&p=1651#p1651

viewtopic.php?f=2&t=49&p=389#p389

viewtopic.php?f=3&t=55

etc.

Posted on: Mon Jan 19, 2015 5:28 pm

Posts: 334
Joined: Wed Apr 16, 2014 9:20 pm
Re: Right to left exponentiation
I do not know if this will help. It is how I think about it.

This issue usually arises when the solutions could be a power (multiple) of 2, 4 and 8

In a cage that takes three elements, the final exponent MUST be a power (multiple) of another number

In todays example, we had the solution of 1024 which is either 2^10 or 4^5

The exponent 10 in not a power of any other digit, so that solution can not work
That leaves 4^5 as the only solution. 5 can only be 5^1.

The solution set for cage is {1, 4, 5}

There was a puzzle recently that had 65536 has the solution.
63356 = 2^16 or 4^ 8

It was also a bent cage of thee elements.

The possible solution sets were
{2, 2, 4} for 2 ^ (4^2) = 2^16 or
{2, 3, 4} for 4 ^ (2^3) = 4^8

So until elimination from other rows forced a solution, one had to keep the numbers (2,3,4) in all three positions of the cage.
I think the correct answer took advantage of the bent (corner) cage and was {2, 4, 2} with the 4 being in the corner of the bent cage

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