I NEED TO FIND A FORMULA THAT WILL GIVE ME THE GREATIST PRODUCT AND
THE SMALLET PRODUCT USING EACH OF THE DIGITS 2 TO 6 EXACTLY ONCE TO BE
USED IN A FORMULA WHERE THREE ON THE NUMBERS ARE MULTIPLIED BY TWO OF
THE NUMBERS |
Request for Question Clarification by
mathtalk-ga
on
28 Nov 2004 19:55 PST
Hi, ayeros-ga:
Are you asking how to arrange the digits 2,3,4,5,6 into a three-digit
and a two-digit number (using each digit only once), so that A) the
product is as large as possible, and re-arranged so that B) the
product is as small as possible?
Is the "formula" you need the same as these two arrangements? Or did
you have something more general in mind?
regards, mathtalk-ga
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Clarification of Question by
ayeros-ga
on
28 Nov 2004 20:02 PST
how to arrange the digits 2,3,4,5,6 into a three-digit
and a two-digit number (using each digit only once), so that A) the
product is as large as possible, and re-arranged so that B) the
product is as small as possible?
Is the "formula" you need the same as these two arrangements?
so yes; is there a formula to get the answer or do i have to just try
each combination and if there is a formula is there just one or are
there more
|
Request for Question Clarification by
mathtalk-ga
on
29 Nov 2004 08:52 PST
Please see the answers provided in a Comment by reined-ga.
I don't know if you consider it a "formula", but there is a principle
behind the arrangement of digits to make the product as large or as
small as possible.
The leading digits of the multiplicand are "most significant". Thus
for the sake of a large product, we should place the two largest
digits in these positions. Also, for a small product, we should place
the two smallest digits in these leading positions.
For the next digit, the proportional increase of a second digit is in
relation to the size of the first digit. For example 64 is less of a
proportional increase over 60 than 54 is over 50. So in placing the
second digit we either maximize the impact of placing our next largest
digit behind the smaller of the two first digits (to get the largest
possible product), or we minimize its impact by placing the next
smallest digit behind the smaller of the two first digits (to get the
smallest possible product). In both cases the position behind the
smaller leading digit has the greatest impact.
Hence for the sake of the largest product, the first four selections would be:
63 * 54
and for the sake of the smallest product, the first four selections would be:
24 * 35
Then you are left with placing the fifth and final digit at one end or
the other number. The same principal applies. Tacking the last 2 on
the end of 54 to make 542 will increase the product more than putting
it behind 63. Putting the 6 behind 35 to make 356 will increase the
product _less_ than putting it behind 24.
regards, mathtalk-ga
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