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Maximize the product (arithmetic level)


Best Answer Pickett, 07 April 2014 - 07:40 PM

Spoiler for First crack

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#1 Perhaps check it again

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Posted 07 April 2014 - 05:59 PM

You will use exactly twelve of the numbers 0.7 and exactly four of the numbers 0.6.

Or, you can just type ".7" and ".6," respectively, if you wish.

Concatenation of the sevens and sixes (mixed or matched) is not allowed).

No other numbers are to be used.

You can use unlimited plus signs.  An unlimited number of

parentheses can be used for both grouping and for

multiplication.  No other symbols or operations may be used.

 

Put these together to form an expression that gives the maximum

value.

 

Here are two examples of the forms:

 

Example 1)

 

(0.7 + 0.7 + 0.7 + 0.7 + 0.7 + 0.7)(0.7 + 0.7 + 0.7 + 0.7 + 0.7 + 0.7)(0.6 + 0.6 + 0.6 + 0.6) =

 

(4.2)(4.2)(2.4) =

 

42.336

 

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 

Example 2)

 

(.7 + .7)(.7 + .7)(.7 + .7)(.7 + .7)(.7 + .7)(.7 + .7)(.6 + .6)(.6 + .6) =

 

[(1.4)^6](1.2)(1.2) =

 

10.843  (approximately)

 

 

 

 

(Let me know if I made any errors, please.)


Edited by Perhaps check it again, 07 April 2014 - 06:00 PM.

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#2 Pickett

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Posted 07 April 2014 - 07:40 PM   Best Answer

Spoiler for First crack


Edited by Pickett, 07 April 2014 - 07:45 PM.

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#3 BMAD

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Posted 08 April 2014 - 01:25 AM

I believe Pickett has it
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#4 bonanova

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Posted 08 April 2014 - 05:23 PM

Pickett has my vote


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




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