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        riddles >> hard >> Determine the missing number
        
(Message started by: gong on May 6^th, 2004, 7:44am)

Title: Determine the missing number
Post by gong on May 6^th, 2004, 7:44am

A real hard one, I have not found out the answer yet. Terribly curious now, hope your guys can solve it!

Title: Re: Determine the missing number
Post by THUDandBLUNDER on May 6^th, 2004, 8:05am

Quote:

A real hard one...

My answer can't be right then. :'(

:[hide]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[/hide]

Title: Re: Determine the missing number
Post by towr on May 6^th, 2004, 9:48am

The numbers don't really seem to correspond with the area from the looks of things.. Maybe circumference.. hmm

Title: Re: Determine the missing number
Post by gong on May 6^th, 2004, 1:10pm

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.

Title: Re: Determine the missing number
Post by THUDandBLUNDER on May 7^th, 2004, 3:21am

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.

Title: Re: Determine the missing number
Post by phobos on May 12^th, 2004, 7:01am

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 [hide] any number [/hide]. 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.

Title: Re: Determine the missing number
Post by gong on May 12^th, 2004, 7:49am

thanks a lot, phobos! I am convinced it is the answer. Your friend is really a genius! The answer should be 49.

Title: Re: Determine the missing number
Post by TenaliRaman on May 14^th, 2004, 10:57am

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

???

Title: Re: Determine the missing number
Post by phobos on May 14^th, 2004, 3:39pm

Oh dear you're absolutely right Tenali!! :o
Man that's embarrassing :P :P :P

Title: Re: Determine the missing number
Post by Three Hands on May 14^th, 2004, 5:11pm

Back to square one, then... ::)

Title: Re: Determine the missing number
Post by grimbal on May 17^th, 2004, 4:12pm

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)

Title: Re: Determine the missing number
Post by THUDandBLUNDER on May 19^th, 2004, 5:05am

on 05/17/04 at 16:12:25, grimbal wrote:

There is no 1. There must be a 1. The missing number is 1.

There is no 8. There must be an 8. The missing number is 8.

Title: Re: Determine the missing number
Post by Leonid Broukhis on May 19^th, 2004, 7:06pm

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?