Captain Kirk has landed the Enterprise in your front yard and invites you onto the holodeck, where you meet a King with a beautiful daughter (aren't they all?) The King wishes to give her hand in marriage only to the wisest of her suitors. So he has devised the following test, and you're first in line. (For puzzle solvers of the female persuasion, the King has a handsome prince ... etc. Actually, you are free to write the prologue in the manner that provides the greatest motivation.)

On the Princess' vanity table sits a ring holder comprising three vertical pegs, each holding a random positive number of royal rings. (Reminiscent of the old Tower of Hanoi puzzle, but here the objective is different.) You must transfer rings from one peg to another, in discrete steps, with the objective of emptying one of the pegs of all its rings. A step consists of doubling the number of rings on some peg using rings from another peg that initially has at least as many rings as the first. Say the rings on two pegs initially number aandb, respectively, wherea is not less thanb. After the move, the pegs will have respectively (a - b) and 2brings. Clearly the winning position occurs when you have two pegs with equal numbers of rings (a=b.) You may make as many moves as you like.

Will you have a pleasurable afternoon on the holodeck? If so, how will you empty one of the pegs?

By the way, when you go home, the Princess stays on the deck.

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## bonanova 85

Captain Kirk has landed the Enterprise in your front yard and invites you onto the holodeck, where you meet a King with a beautiful daughter (aren't they all?) The King wishes to give her hand in marriage only to the wisest of her suitors. So he has devised the following test, and you're first in line. (For puzzle solvers of the female persuasion, the King has a handsome prince ... etc. Actually, you are free to write the prologue in the manner that provides the greatest motivation.)

On the Princess' vanity table sits a ring holder comprising three vertical pegs, each holding a random positive number of royal rings. (Reminiscent of the old Tower of Hanoi puzzle, but here the objective is different.) You must transfer rings from one peg to another, in discrete steps, with the objective of

emptying one of the pegsof all its rings. A step consists ofdoubling the number of rings on some pegusing rings from another peg that initially has at least as many rings as the first. Say the rings on two pegs initially numberanda, respectively, wherebis not less thana. After the move, the pegs will have respectively (b-a) and 2brings. Clearly the winning position occurs when you have two pegs with equal numbers of rings (b=a.) You may make as many moves as you like.bWill you have a pleasurable afternoon on the holodeck? If so, how will you empty one of the pegs?

By the way, when you go home, the Princess stays on the deck.

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