Thought Exercise
On an archeological dig near the highlands of Tibet, Alley discovered an ancient oil lamp. Just for laughs she rubbed the lamp. She quickly stopped laughing when a huge puff of magenta smoke spouted from the lamp, and an ornery genie named Murray appeared. Murray, looking at the stunned Alley, exclaimed, “Well, what are you staring at? Okay, okay, you’ve found me; you get your three wishes. So, what will they be?” Alley, although in shock, realized she had an incredible opportunity. Thinking quickly, she said, “I’d like to find the Rama Nujan, the jewel that was first discovered by Hardy the High Lama.” “You got it,” replied Murray, and instantly nine identical-looking stones appeared. Alley looked at the stones and was unable to differentiate any one from the others.
Finally she said to Murray, “So where is the Rama Nujan?” Murray explained, “It is embedded in one of these stones. You said you wished to find it. So now you get to find it. Oh, by the way, you may take only one of the stones with you, so choose wisely!” “But they look identical to me. How will I know which one has the Rama Nujan in it?” Alley questioned. “Well, eight of the stones weigh the same, but the stone containing the jewel weighs slightly more than the others,” Murray responded with a devilish grin.
Alley, becoming annoyed, whispered under her breath, “Gee, I wish I had a balance scale.” Suddenly a balance scale appeared. “That was wish two!” declared Murray. “Hey, that’s not fair!” Alley cried. “You want to talk fair? You think it’s fair to be locked in a lamp for 1729 years? You know you can’t get cable TV in there, and there’s no room for a satellite dish! So don’t talk to me about fair,” Murray exclaimed. Realizing he had gone a bit overboard, Murray proclaimed, “Hey, I want to help you out, so let me give you a tip: That balance scale may be used only once.” “What? Only once?” she said, thinking out loud. “I wish I had another balance scale.” ZAP! Another scale appeared. “Okay,kiddo, that was wish three,” Murray snickered. “Hey, just one minute,” Alley said, now regretting not having asked for one million dollars or something more standard. “Well at least this new scale works correctly, right?” “Sure, just like the other one. You may use it only once.” “Why?” Alley inquired. “Because it is a ‘wished’ balance scale,” he said, “so the rule is ‘one scale, one balancing’; it’s just like the rule against using one wish to wish for a hundred more wishes.” “You are a very obnoxious genie.” “Hey, I don’t make up the rules, lady, I just follow them,” he said.
So, Alley may use each of the two balance scales exactly once. Is it possible for Alley to select the slightly heavier stone containing the Rama Nujan from among the nine identical-looking stones? Explain why or why not.
Alley, becoming annoyed, whispered under her breath, “Gee, I wish I had a balance scale.” Suddenly a balance scale appeared. “That was wish two!” declared Murray. “Hey, that’s not fair!” Alley cried. “You want to talk fair? You think it’s fair to be locked in a lamp for 1729 years? You know you can’t get cable TV in there, and there’s no room for a satellite dish! So don’t talk to me about fair,” Murray exclaimed. Realizing he had gone a bit overboard, Murray proclaimed, “Hey, I want to help you out, so let me give you a tip: That balance scale may be used only once.” “What? Only once?” she said, thinking out loud. “I wish I had another balance scale.” ZAP! Another scale appeared. “Okay,kiddo, that was wish three,” Murray snickered. “Hey, just one minute,” Alley said, now regretting not having asked for one million dollars or something more standard. “Well at least this new scale works correctly, right?” “Sure, just like the other one. You may use it only once.” “Why?” Alley inquired. “Because it is a ‘wished’ balance scale,” he said, “so the rule is ‘one scale, one balancing’; it’s just like the rule against using one wish to wish for a hundred more wishes.” “You are a very obnoxious genie.” “Hey, I don’t make up the rules, lady, I just follow them,” he said.
So, Alley may use each of the two balance scales exactly once. Is it possible for Alley to select the slightly heavier stone containing the Rama Nujan from among the nine identical-looking stones? Explain why or why not.