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# Tower of power

78 replies to this topic

### #1 bonanova

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Posted 06 October 2008 - 05:55 AM

Take a variable x and raise it to the xth power: xx; call the result y.
Now raise x to the y power: xy; call that result y. i.e. replace the previous value of y with the value of xy.
Again, raise x to the y power: xy; and replace the previous value of y with the value of xy.

Repeat this an arbitrarily large number of times, and set the result equal to 2.
That creates the infinite exponential sequence

x to the x to the x to the x to the x to the x .... = 2.

What value of x, if any, satisfies the equation?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #2 Supandi

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Posted 06 October 2008 - 06:26 AM

After some jugglery in Excel and a bit of Googleing

Spoiler for Can't say I've understood any of it though.

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### #3 bonanova

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Posted 06 October 2008 - 07:49 AM

After some jugglery in Excel and a bit of Googleing

Spoiler for Can't say I've understood any of it though.

Hi Supandi,

Nice going.
But you all know how much I love "showing your work" even tho sometimes I don't.

So let me expand the puzzle.
• Prove it [elegantly]
• Do any other values of x satisfy the equation?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #4 Yoruichi-san

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Posted 06 October 2008 - 09:34 AM

Lol...this is TANTALIZING!
I was totally reading the problem wrong at first...but now I think I get it...

I'm not sure how solid this is...I'm not sure how sound the assumption inf-1=inf is, but...

Spoiler for What I've got...

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Women are definitely stronger. We are [Fe]males, after all...

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### #5 octopuppy

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Posted 06 October 2008 - 09:58 AM

Spoiler for Proof (sort of)

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### #6 woon

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Posted 06 October 2008 - 10:13 AM

Hi Supandi,

Nice going.
But you all know how much I love "showing your work" even tho sometimes I don't.

So let me expand the puzzle.

• Prove it [elegantly]
• Do any other values of x satisfy the equation?

If there is another value,
Spoiler for It must be

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### #7 Supandi

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Posted 06 October 2008 - 12:42 PM

Hi Supandi,

Nice going.
But you all know how much I love "showing your work" even tho sometimes I don't.

So let me expand the puzzle.

• Prove it [elegantly]
• Do any other values of x satisfy the equation?

Sure.

Its exactly what Octopuppy said. I couldn't have said it better.

Infact I couldn't have said it at all I'm kinda math illiterate
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### #8 Chuck Rampart

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Posted 06 October 2008 - 02:01 PM

Spoiler for Proof (sort of)

I don't think you need the "sort of" in there. Good work.
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### #9 bonanova

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Posted 06 October 2008 - 02:06 PM

Lol...this is TANTALIZING!
I was totally reading the problem wrong at first...but now I think I get it...

I'm not sure how solid this is...I'm not sure how sound the assumption inf-1=inf is, but...

Spoiler for What I've got...

Very astute; and inf-1 is in fact inf, for the purposes of this riddle.
Spoiler for Which leads to this cute solution
Before I declare Y-san, octopuppy and woon as solvers, however, and this is where it really becomes tantalizing:

Is there yet another value of x which satisfies the equation?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #10 octopuppy

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Posted 06 October 2008 - 03:08 PM

Very astute; and inf-1 is in fact inf, for the purposes of this riddle.

Spoiler for Which leads to this cute solution
Before I declare Y-san, octopuppy and woon as solvers, however, and this is where it really becomes tantalizing:

Is there yet another value of x which satisfies the equation?

Spoiler for You mean...

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