Andy Latto asks whether the operation "pour from glass B into glass A until A is at the same level as A' (where A and A' are identical)" is permitted; yes, I should have included it. Jim Propp On Tue, Mar 20, 2018 at 3:11 PM, James Propp <jamespropp@gmail.com> wrote:
Oh yeah, I should've included that operation in the repertoire of permitted moves.
One might also wish to allow a version of this move in which the second glass is smaller than the first, and one is allowed to fill the second glass. (As in those well-known problems in which one implements a constrained version of the Euclidean algorithm by passing fluid back and forth between containers.)
Jim Propp
On Tue, Mar 20, 2018 at 2:59 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
PROBLEM: Show that even if the two empty glasses were different shapes from one another (and from the identical full glasses), one can still divide the lassi into four equal portions. The only allowed operation is to equalize the amount of lassi in two glasses of the same shape by equalizing the height of the lassi. (One might quibble that in practice you can only do this approximately, but for purposes of this puzzle, ignore that nicety.)
I presume there is a second allowed operation, which is to transfer all of the fluid from one glass into another (irrespective of the shape of the source and target glasses), provided doing so does not cause an overflow error in the target glass...?
-- APG.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun