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        riddles >> putnam exam (pure math) >> Mathematical Principle needed unknown
        
(Message started by: B.R on Dec 27^th, 2004, 12:33pm)

Title: Mathematical Principle needed unknown
Post by B.R on Dec 27^th, 2004, 12:33pm

If I buy a certain 4 items priced at:
$1.20
$1.25
$1.50
$3.16

- To get the total of these figures, it does not matter
if the prices are added together as one would expect or
if the prices are multiplied. The total bill will be the
same: $7.11. What mathematical principle is being
displayed in this problem?

What'dya Reckon?

Title: Re: Mathematical Principle needed unknown
Post by Icarus on Dec 27^th, 2004, 2:58pm

The only principle I see is the principle that if you have at least as many unknowns as equations, you generally have solutions (not always - sometimes the only possible solutions for all but one of the equations turn out to all be outside the domain of the remaining equation).

Title: Re: Mathematical Principle needed unknown
Post by John_Gaughan on Dec 29^th, 2004, 11:43am

Although I cannot see a direct relationship, this reminds me of the Golden (http://en.wikipedia.org/wiki/Golden_ratio) Ratio (http://mathworld.wolfram.com/GoldenRatio.html).

Title: Re: Mathematical Principle needed unknown
Post by THUDandBLUNDER on Dec 29^th, 2004, 8:51pm

on 12/29/04 at 11:43:47, John_Gaughan wrote:

Although I cannot see a direct relationship, this reminds me of the Golden (http://en.wikipedia.org/wiki/Golden_ratio) Ratio (http://mathworld.wolfram.com/GoldenRatio.html).

With two variables we have
x₁x₂ = x₁ + x₂
This equation is satisfied by
x₁ = Phi, x₂ = Phi²

Of course, this 'solution' does not satisfy the physical constraints of the puzzle, which are (with n variables):
for i = 1 to n
100x_i [in] [bbz]⁺
and
100[smiley=prod.gif]x_i [in] [bbz]⁺

Given the first constraint, the chance of satisfying the second constraint decreases as n increases.