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Topic: Approximating 82 (a puzzle from 1882(?)) (Read 1027 times) |
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BNC
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Approximating 82 (a puzzle from 1882(?))
« on: Oct 8th, 2003, 11:40pm » |
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This is (supposedly) a famous puzzle from 1882, that was assigned a $1000 aword back then. I didn't hear about it before, but that's won't be a first...
OK, the puzzle is:
use the numbers 4,5,6,7,8,9,0 (each once) and eight dots to form numbers. The addition of these numbers should be as close to 82 as possible.
The dots have a special meaning here:
1. They are used in the normal way to represent the decimal point. 0 is not required for <1 fractions, e.g., 1/2 is .5 .
2. They are used to represent infinite repeating numbers, by placing a dot above a number. To keep the representation simple here, I suggest we'll adopt a symbol for that -- instead of writing 2 with a dot on top, we'll write 2^ (which means we have 8 "."s and "^"s together).
For example, 1/3 would be .3^
If more than a single digit need to be repeated, a dot is placed on top of the first recurring digit, and another on top of the last. For example, 1/7 would be .1^42857^
So, how close can you get to 82?
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TenaliRaman
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #1 on: Oct 9th, 2003, 6:44am » |
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ok my first attempt,
74.6^,5.0^,.8^,.9^
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visitor
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #2 on: Oct 9th, 2003, 9:06am » |
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Is 81.999999999... close enough?
80.4^7^, .5^, .9^6^
Where's my money?
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James Fingas
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #3 on: Oct 9th, 2003, 9:12am » |
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on Oct 8th, 2003, 11:40pm, BNC wrote:So, how close can you get to 82?
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Pretty damn close!
80.4^6^ + .5^ + .9^78^ = 81.9^99180^
There's probably a way to improve this somehow...
Doh! Looks like visitor has me beat ...
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| « Last Edit: Oct 9th, 2003, 9:13am by James Fingas » |
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BNC
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #4 on: Oct 9th, 2003, 9:19am » |
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on Oct 9th, 2003, 9:06am, visitor wrote:Is 81.999999999... close enough?
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I guess... Now just answer this: which statement is correct?
A. 81.999... < 82
B. 81.999... = 82
C. 81.999... > 82
Quote:
Oh, that's the easy part. Just finish the time-machine you've building in your garage, and go get it!
Well done, visitor!
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TenaliRaman
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #5 on: Oct 9th, 2003, 9:32am » |
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is .4^7^ valid 
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BNC
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #6 on: Oct 9th, 2003, 9:58am » |
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on Oct 9th, 2003, 9:32am, TenaliRaman wrote:is .4^7^ valid
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Why wouldn't it be!? That's 0.474747474...
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TenaliRaman
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #7 on: Oct 9th, 2003, 10:04am » |
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shouldn't .47474747... be written as .^47^ ??
However i checked with visitors calculation and i got that he meant 0.4747474747474747.....(the notation got me confused that's all!!)
Cheers!!!! (Kudos to visitor btw!)
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Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
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James Fingas
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #8 on: Oct 9th, 2003, 10:57am » |
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Doh! No wonder I couldn't get it right ... I had an extra '8' in there 
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SWF
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #9 on: Oct 9th, 2003, 7:50pm » |
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The first solution I found was different from vistor's, but now it is clear that several solutions can be generated from a single solution. From visitors solution the portions to the right of the decimal place may be paired with the eighty or the eighty can stand alone with no dot after it.
That was pretty simple, but a more interesting variation is to switch the digits around. In the .474747 + .555555 + .969696 of visitor's solution, note that the values in each position add to 18 to give 1.9999999. Any ordering of those digits keeping the 7&6 and the 4&9 paired with each other will work. For example, .5555555 + .797979 + .646464 or .55555 + .747474 + .696969.
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Frodo
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9 Dots Riddle, and its follow up riddle
« Reply #10 on: Mar 30th, 2004, 10:56am » |
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To solve the 9 dots puzzle as given, you have to "think outside the box". If the dots are numbered 1-9 from top left in rows, one line will pass diagnally through dots 6 & 8, and extend on both sides to lines that pass horizontally through the first row, and vertically through the first column. The last line passes through dots 1, 5, and 9.
Now, can you join 9 dots in the same configuration with only 3 lines?!?!
HINT: These are "dots". Not "points". Hmmm..have to research how to post a hint that you have to hightlight. :-P
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Icarus
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #11 on: Mar 30th, 2004, 3:38pm » |
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Unfortunately, moderator powers do not extend to moving individual posts, only entire threads. 
Frodo: This thread has absolutely nothing to do with the problem you are refering to. The thread you should post that reply to is Nine Dots, Three Lines.
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Grimbal
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #12 on: Apr 23rd, 2004, 4:40pm » |
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on Oct 9th, 2003, 9:19am, BNC wrote:Now just answer this: which statement is correct?
A. 81.999... < 82
B. 81.999... = 82
C. 81.999... > 82 |
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81.999... = 82
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Icarus
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Re: Approximating 82 (a puzzle from 1882(?))
« Reply #13 on: Apr 24th, 2004, 7:03am » |
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Gimbal - BNC was being facetious. The longest thread in these forums is 0.999... thread in the Medium forum. Every so often someone new comes along and tries to argue that 0.999... < 1.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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