Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 196

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MetaDriver:

I also found a hole. Six (2*3) as a setter is weak. You need 18 (=2*3*3). // Counterexample for the top formula: n = 2;

There seems to be no holes now: group A+B = 2 + n*18. Correspondingly, group X+Y+Z = 2000 - ( 2 + n*18 ), where n is in the range 0...55.

That leaves a total of 56 solutions.

In fact all solutions except n=0. In short, Sergey (Contender) was right, the solution with two weightings is the only one: 1+1 + 666+666+666. Amen.

TheXpert:
One comparison )

"I don't believe it" (c) K. Stanislavsky.

Come on, show me what you got, I'll show you a hole. :)

 
TheXpert:
One comparison )
Agreed!
 
MetaDriver:


"I don't believe it" (c) K. Stanislavsky

Come on, show me what you've come up with, I'll show you a hole. :)


One comparison is enough!

Are you sure you don't want to figure it out yourself already? ;)

 
Contender:


One comparison is enough!

Are you sure you don't want to figure it out yourself already? ;)

Under so much pressure I have to agree. ;)

// One solution for sure. No others are in sight yet. Looks like the only one.

 
MetaDriver:

Under so much pressure, I have to agree. ;)

// One solution for sure, no others seem to be in sight yet.

:))

We divide it into 3 piles: 667 + 667 + 666?

 
Contender:

:))

We divide it into 3 piles: 667 + 667 + 666?

by three, but not like this: 666+666+668

;)

 
MetaDriver:

by three, but not like this: 666+666+668

;)

So the solution is not one, but one and a half ;)
 
Contender:
So the solution is not one, but one and a half ;)
No, it's not one and a half... Exactly one. // The reverse sequence is holes.
 

sanyooooook: блин математики давайте хоть какой нить срок выполнения задачи после которого вы предоставляете ответ, а то я про ферзей до сих пор решаю )

The answer will be in your personal message as soon as you ask.

MetaDriver : 2. Divide the remaining group into three equal heaps X, Y, Z (1998/3 = 666). Weigh the two heaps (X and Y). If different - problem solved, if identical - also solved [X and Z] and [Y and Z] guaranteed different.
I missed it: each heap of 666 can have 333 balls of both types. They are equal.
 
Contender:

Yes, the short solution does indeed seem to be the only one:

1+1+666+666+666 and 2 weighing.

Prove that in one weighing is impossible. Zadachas of such type on braingames.ru must be justified - if it is not specially mentioned that it is not necessary to prove minimalism.

Or show how a single weighing can be done. You certainly can't do without weighing :)

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