qts@houxa.UUCP (J.RAMMING) (02/14/86)
keywords: marbles, hacksaw ******* Here is a puzzle I ran across several years ago; it hasn't made the rounds lately, so I thought I would post it. Given: an ordinary balance, and twelve marbles. Of these twelve marbles, 11 of them have exactly the same weight. The twelfth marble is EITHER lighter OR heavier than the other eleven. We do not know, at the outset, which marble it is, or whether it is lighter or heavier. Puzzle 1: Suppose the balance spontaneously explodes after it has been used three times. Your task is to determine, in the three weighings available, which is the odd marble out, and whether it is lighter or heavier than its companions. Puzzle 2: Prove that three weighings is insufficient for the above, when one starts off with 14 marbles. Puzzle 3: (For twisted minds): Find the odd marble out, and figure out whether it is lighter or heavier, starting with 13 marbles. (Might need an extra tool or two...) J. Christopher Ramming UUCP: decvax!bellcore!houxa!qts WORK: (201) 949-9531 HOME: (201) 542-2079
john@cisden.UUCP (John Woolley) (02/18/86)
In article <952@houxa.UUCP> qts@houxa.UUCP (J.RAMMING) writes: >Given: an ordinary balance, and twelve marbles. Of these twelve > marbles, 11 of them have exactly the same weight. The > twelfth marble is EITHER lighter OR heavier than the other > eleven. We do not know, at the outset, which marble it > is, or whether it is lighter or heavier. > >Puzzle 1: Suppose the balance spontaneously explodes after it has > been used three times. Your task is to determine, in the > three weighings available, which is the odd marble out, and > whether it is lighter or heavier than its companions. Yes, this can be done. >Puzzle 2: Prove that three weighings is insufficient for the above, > when one starts off with 14 marbles. This also is true. >Puzzle 3: (For twisted minds): Find the odd marble out, and figure > out whether it is lighter or heavier, starting with 13 > marbles. (Might need an extra tool or two...) This is not possible. With 13, you can find which one is off-weight in 3 steps, but there's 1 chance in 13 that you won't be able to tell which way off it is. (That in itself constitutes a hint.) And now a miraculously wonderful generalization. (I'll answer in a couple of weeks.) Puzzle 4: (For very twisted minds.) Determine how many marbles you can solve the puzzle for in n weighings, as a function of n. This is not easy. Puzzle 5: (Just take a guess. Answer follows from 4.) How many weighings would it take with 1000 marbles? -- Peace and Good!, Fr. John Woolley "Compared to what I have seen, all that I have written is straw." -- St. Thomas