OT: "82" puzzle

[Maple Leafs]

Standard QuickSand disclaimer: I didn't create this puzzle, but I like it.

Standard Maple Leafs disclaimer: Every time I post a puzzle here, someone points out that they've already seen that one, it was posted back in June of '99, etc. So this puzzle is exclusively for people who haven't seen it already, OK? Not everyone has been on the board since the beginning, Methuselah.

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This is a famous problem from 1882, to which a prize of $1000 was awarded for the best solution. The task is to arrange the seven numbers 4, 5, 6, 7, 8, 9, and 0, and eight dots in such a way that an addition approximates the number 82 as close as possible. Each of the numbers can be used only once. The dots can be used in two ways: as decimal point and as symbol for a recurring decimal. For example, the fraction 1/3 can be written as:

.
. 3

The dot on top of the three denotes that this number is repeated infinitely. If a group of numbers needs to be repeated, two dots are used: one to denote the beginning of the recurring part and one to denote the end of it. For example, the fraction 1/7 can be written as:

. .
. 1 4 2 8 5 7

Note that '0.5' is written as '.5'.

The Question: How close can you get to the number 82?

[cuervo72]

Ok: how's this:

. .. ..
80 .5 .74 .69


Darn, getting these to line up is tough....

[Maple Leafs]

Very well done. Actually, that's not even the answer I had, so you get bonus points.

[cuervo72]

Cool. I think I'll let someone else come up with whatever the other answer is :)

[Celeval]

Well, by the strict rules: "Each of the numbers can be used only once."

Since they 'can' be used only once, it implies you don't need to use them all... although if that was the case, then:

<PRE>
. .
76.0 (+) 5.9
</PRE>

Which equals 81.9999..., mathematically equal to 82. Of course, that only still leaves 4 periods and two numbers, so I know I'm wrong. ;)
Kevin

[Maple Leafs]

Originally posted by Celeval
Well, by the strict rules: "Each of the numbers can be used only once."

Since they 'can' be used only once, it implies you don't need to use them all... Interesting... I guess that could count, although the rules do imply that you're supposed to use them all.

P.S. Shouldn't you be off rigging another playoff series?

[AnalBumCover]

Originally posted by cuervo72

. .. ..
80 .5 .74 .69


Without looking at cuervo's answer above, I got something VERY similar... :P


. .. ..
80 .5 .47 .96


Ugh.

[Maple Leafs]

That was the "official" answer I had.

[QuikSand]

Neat puzzle.. sorry I basically missed it. We certainly could derive new ones based on basically the same concept, though.

Originally posted by Maple Leafs
The task is to arrange the seven numbers 4, 5, 6, 7, 8, 9, and 0, and eight dots in such a way that...

To me, this does more than "imply" you have to use all seven numerals, it flat out says so.

[AnalBumCover]

Originally posted by Maple Leafs
That was the "official" answer I had.
WooHoo! :D

[cuervo72]

Originally posted by Maple Leafs
That was the "official" answer I had.

Oh yeah, I guess I could have posted that too; I figured they were basically the same as flipping the last digits like that will I think always yield the same result (something transitive going on there).

[AnalBumCover]

Other correct similar answers:


. .. ..
80 .5 .79 .64

. .. ..
80 .5 .46 .97


Just a matter of flipping digits around, like cuervo said.

[QuikSand]

You know, I confess I didn't work through this problem... but think about it. $1000 in 1882 was a boatload of money... someone got that kind of cash for solving this puzzle? There really isn't all that much to it, seems to me.

[AnalBumCover]

Originally posted by QuikSand
You know, I confess I didn't work through this problem... but think about it. $1000 in 1882 was a boatload of money... someone got that kind of cash for solving this puzzle? There really isn't all that much to it, seems to me.

That's what I was thinking. If I could solve this, then anyone could! I'll be expecting my $1G in the mail shortly.

[Celeval]

Originally posted by Maple Leafs
P.S. Shouldn't you be off rigging another playoff series?

Hey, just because your guys forgot how to hit; that's not my fault. :)

Kevin