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Guest Message by DevFuse
 

Prime

Member Since --
Offline Last Active Dec 03 2013 05:53 PM
-----

Topics I've Started

Weighing Problem Resurected

23 February 2013 - 02:05 AM

You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

 

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many  stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.
 

HISTORICAL NOTE:

This problem originated on Brain Den. I constructed it based on Bonanova's problem Weighty  Thoughts: http://brainden.com/...4932--/?p=84107 few years ago.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.


One's divisibility

09 February 2013 - 08:34 PM

Find the smallest number consisting of only "1"-s,

which would be divisible by "333...3" (one hundred "3"-s.)

(Decimal system.)


1966

08 February 2013 - 06:44 AM

All numbers from 1 to 1966 are written on a blackboard.

You are allowed to erase any two numbers and write their difference instead.

Prove that repetition of that operation may not result in having only zeroes on the blackboard.


(Problem from Russian Math Olympiads. 6-th grade, 1966.)


Origins of Tetris?

07 February 2013 - 09:03 PM

Prove that you cannot
cover a 10 x 10 chessboard with 25 figures

Attached File  Tfig.gif   914bytes   135 downloads


(Problem from Russian Math Olympiads. 6-th grade, 1964.)


Can't sign out

01 February 2013 - 08:13 AM

Does anyone else experience this problem?

When in IE9 I cannot sign out unless I manually delete all cookies for BD Domain.

In Chrome it appears to sign me out. But after I close the browser, then open it again and go to BD Forums, I find myself signed on.