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Highest Number (Posted on 2004-09-18) Difficulty: 2 of 5
Use all the digits 1 to 9 create three 3-digit numbers, which, when multiplied together creates the highest value possible.

See The Solution Submitted by SilverKnight    
Rating: 3.1250 (8 votes)

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re(3): How to do! | Comment 6 of 19 |
(In reply to re(2): How to do! by Juggler)

I am not quite sure what you mean.  It sounds to me that you are putting forth an argument of the form:

Given condition A, quantity Q takes a maximum when condition B holds.

Thus, for any condition A' that is similar (semantically?) to A, we have that, given condition A', quantity Q again takes a maximum when condition B holds.

(here, we have specifically

A="sum of numbers is fixed"
A'="sum of digits is fixed"
Q="product of numbers"
B="numbers are all equal"


If that is your argument, it certainly falls short of a verification.  It is at best solid intuition.

  Posted by David Shin on 2004-09-18 15:18:02
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