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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1328.0. "Elementary maxes and mins with digit sets" by EAGLE1::BEST (R D Best, sys arch, I/O) Wed Nov 07 1990 11:24

Here's an elementary number experiment that I found produces a surprising
result (read 'defied my first several intuitions').  I lifted it from a
recent Newsweek article on proposed changes to elementary mathematics
curriculum.

	Choose any 5 digits.  Break them into a two digit and a three digit
	number.  What is the largest product that can be formed from these ?
	The smallest ?

{ I can't recall if the article made clear whether, in the second part,
the same five digits used in the first part were to be rearranged, or if
a new set of 5 was to be chosen.  I also can't recall whether the problem
spec'd different digits, but it's not interesting at all without that
requirement. }
T.RTitleUserPersonal
Name		DateLines
1328.1Just off the top of my head:CHOVAX::YOUNGThe OOL's are not what they seem.Wed Nov 07 1990 17:185
    My intuition says 875*96 and 245*13.  (excluding 0 as a digit).
    
    ?
    
    --  Barry
1328.2reality is so annoying :-)EAGLE1::BESTR D Best, sys arch, I/OWed Nov 07 1990 17:5330
>    <<< Note 1328.1 by CHOVAX::YOUNG "The OOL's are not what they seem." >>>
>                       -< Just off the top of my head: >-
>
>    My intuition says 875*96 and 245*13.  (excluding 0 as a digit).
>    
>    ?

You've got better intuition than I do.  My initial (mindless) guess was
"Well of course it's got to be 987 * 65" (make the big number as big as
possible).  Then I noticed that I could make the result a good bit bigger
by swapping the 8 and the 6 yielding 967 * 85 (barely changes the value
of 987, but cranks up the 65 significantly).

My next thought was "Aha ! Of course !  Swap the 6 and 7 to make it bigger.
(yields 976 * 85) Gee, it looks like it gets even bigger if I alternate
the sorted digits between the two numbers ( 975  * 86 ).  At this point
I thought I was done, but decided to mess around just to see what else was
possible.

To my chagrin, I discovered Barry's solution.  Damn ! Another neat obvious
pattern into the dumper.

About the only general pattern I can infer is that all digits within a number
must descend (otherwise you could always make a bigger product by switching
a higher valued digit to a higher power-of-ten position).

Any interesting general patterns for other cases ?  how about 6 digits split
3 & 3, and 2 & 4 ?

>    --  Barry