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Topic: Determine the missing number (Read 5748 times) |
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gong
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A real hard one, I have not found out the answer yet. Terribly curious now, hope your guys can solve it!
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ThudnBlunder
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Re: Determine the missing number
« Reply #1 on: May 6th, 2004, 8:05am » |
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My answer can't be right then. 
:60 + 43 + 55 + 30 + 42 + 47 + 62 + 74 + 42 + 41 + 57 + 49 + 66 + 33 + 56 = 757
Perhaps the answer is meant to make the total area a perfect square.
The next highest square number = 784 = 282
Hence smallest solution = 784 - 757 = 27
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| « Last Edit: May 6th, 2004, 10:17am by ThudnBlunder » |
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towr
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Re: Determine the missing number
« Reply #2 on: May 6th, 2004, 9:48am » |
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The numbers don't really seem to correspond with the area from the looks of things.. Maybe circumference.. hmm
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Wikipedia, Google, Mathworld, Integer sequence DB
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gong
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Re: Determine the missing number
« Reply #3 on: May 6th, 2004, 1:10pm » |
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Intuitively, I think the number in each patch should be dertermined by those numbers surrounding it and the contacting sides may have some relation with the wigtht of each number. I have tried the cases I could envision, all failed flatly,  . Maybe the shape of patch, in addition to the number of sides, also plays a role in it.
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| « Last Edit: May 6th, 2004, 1:11pm by gong » |
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ThudnBlunder
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Re: Determine the missing number
« Reply #4 on: May 7th, 2004, 3:21am » |
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It could be argued that the numbers are in proportion to their perimeters.
However, 49 seems too large.
And 62 and 66 seem too small compared with 55, 56, and 57.
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| « Last Edit: May 12th, 2004, 9:00am by ThudnBlunder » |
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phobos
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Re: Determine the missing number
« Reply #5 on: May 12th, 2004, 7:01am » |
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My guess (not me, really (is my friend who'd solved it (but I thought it would be cool to post a solution (and don't forget, in this way I won't look bad for posting a wrong answer)))) would be any number . Take any three touching pieces (a,b,c), sum of the differences: (b-a) and (c-a) will always constitute to the difference (b-c).
Solution is credited to my witty friend Mr. Ukrit Mankong.
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| « Last Edit: May 12th, 2004, 7:02am by phobos » |
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gong
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Re: Determine the missing number
« Reply #6 on: May 12th, 2004, 7:49am » |
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thanks a lot, phobos! I am convinced it is the answer. Your friend is really a genius! The answer should be 49.
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TenaliRaman
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Re: Determine the missing number
« Reply #7 on: May 14th, 2004, 10:57am » |
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u sure there phobos?
(a,b,c)=(33,56,57)
b-a=56-33=23
c-a=57-33=24
sum of b-a and c-a = 47 != b-c?
and if u meant difference of b-a and c-a, then its no surprise
for any three numbers a,b,c
(b-a)-(c-a)=b-a-c+a=b-c
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phobos
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Re: Determine the missing number
« Reply #8 on: May 14th, 2004, 3:39pm » |
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Oh dear you're absolutely right Tenali!! 
Man that's embarrassing 
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Three Hands
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Re: Determine the missing number
« Reply #9 on: May 14th, 2004, 5:11pm » |
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Back to square one, then... 
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Grimbal
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Re: Determine the missing number
« Reply #10 on: May 17th, 2004, 4:12pm » |
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There is no 1. There must be a 1. The missing number is 1.
proof:
http://www.maybach.ru/en/news_418.html
(Rolls-Royce opens at 1, Red Square)
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ThudnBlunder
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Re: Determine the missing number
« Reply #11 on: May 19th, 2004, 5:05am » |
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on May 17th, 2004, 4:12pm, grimbal wrote:| There is no 1. There must be a 1. The missing number is 1. |
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There is no 8. There must be an 8. The missing number is 8.
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Leo Broukhis
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Re: Determine the missing number
« Reply #12 on: May 19th, 2004, 7:06pm » |
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A few random observations.
The "lengths" of sides (computed as sums of values of pieces touching a side) are 240, 170 (full), 179 + ?, and 89 + ?. 240 - 179 = 61, 170 - 89 = 81.
The sum of pieces that do not touch a side is 227, which is, incidentally, a prime. The sum of the remaining pieces is 530 + ?.
And what about the fact that the only two pieces locked together (in 2D) are 66 and the missing one?
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