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Logic, Reason and Critical Thinking, Class 11: Period 4, Thursday, November 19

"Good afternoon, class," Miss Bennet said warmly. "As you well know, we have, of late, been discussing problem-solving. Today I thought it might be interesting for us to apply some of the principles we've been working on."

She uncovered the blackboard to reveal a great deal of writing.

1. Suppose there is a coin inside a bottle, and further suppose someone places a cork into the mouth of the bottle. How can one retrieve the coin without either pulling out the cork or smashing the bottle?

2. Your sock drawer contains ten pairs of white socks and ten pairs of black -- no other colors. Suppose your roommate prefers to sleep in, and you kindly choose socks in the darkness each morning. How many socks must you take from the drawer to ensure your socks for today will match?

3. A gentleman has passed on, and left his wine-cellar to his three devoted sons. In the wine cellar were seven full barrels of wine, seven half-full barrels, and seven empty barrels. His will only asked that the three split the wine equally -- each must have the same number of full, half-full, and empty barrels. There are no measuring devices handy, and yet the father's request is accomplished. How?

4. All of my flowers but two are roses. All of my flowers but two are tulips. All of my flowers but two are daisies. How many flowers do I have?

5. On a table before you are eight jelly donuts, and a balancing scale. Inside one of them is a diamond ring, placed there by the king. The king states that he will give you the ring if you can correctly tell him which jelly donut has the ring. You may not open any of the donuts, and you may only use the scale twice. How will you succeed?

6. Mary's mother has four children. The eldest is named April; the next, May, and the one following that, June. What is the youngest child's name?

7. A horse is tied to a fifteen-foot-long rope. There is a bale of hay twenty-five feet away from him. Yet the horse is able to eat the hay comfortably. Why?

8. Three men arrange to stay at a hotel for the evening; the room rate is thirty dollars, so each contributes ten. After the men have settled in, the manager realizes he overcharged them -- their room should have been twenty-five, not thirty. He gives the bellboy five dollars to return to the men. The bellboy, being devious, gives each man one dollar and pockets the remaining two. Thus, each man paid nine dollars, for a total of twenty-seven. The bellboy took two. Where is the missing dollar?

"There are logical answers to each of these," Miss Bennet assured them. "This is not a quiz. I would like for us to discuss these puzzles together and see if we can arrive upon the solutions. And I will give hints, but only if you ask very nicely."

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With the icon that has the longest keyword(s).

Ponder the questions, take notes, be happy that she skipped the poem about St. Ives. (Or sad, if you are particularly fond of it.)

Suggest answers, or reasonable guesses. Ask questions to clarify terms. Ping one another freely and build upon one another's thoughts.

Edited 2009-11-19 19:11 (UTC)

Do you believe these are helpful for learning problem-solving? Are any of the riddles what you would consider 'unfair' for one reason or another? Have they at least convinced you to re-examine your own preconceptions in addressing problems?

Edited 2009-11-19 19:11 (UTC)

Should they be here.

For she is indeed here.

once_a_traitor suggested this class idea and is, therefore, my hero.

None of these are lateral-thinking puzzles, since those seemed to be unfair and/or off-topic, but I'm actually very fond of lateral-thinking puzzles.

I'll post answers if anyone is stumped OOC but most of these I gathered from various web sources (although Miss Bennet did insist on prettifying the language here and there), so googling should get you all you need.

Edited 2009-11-19 19:16 (UTC)

Leto Atreides

Triela

Triela frowned thoughtfully, mulling over the riddles, before speaking up. "It seems like a lot of these work by making you think they're saying more than they really are..." She sounded almost hesitant, as if she weren't sure she was right.

"You're right," Miss Bennet said, giving the girl what she hoped was an encouraging smile. "Not all of them. Some of them simply involve deduction, or reasoning out a solution based on the situation as presented. But at least one of them is quite clearly toying with preconceptions that are not stated in the problem itself, and another is a bit of verbal sleight-of-hand."

Liz Sherman

Jonothon Starsmore

Jono eyed the riddles for a moment, and then shrugged.

//Th'youngest gel's name is Mary. The question says so itself. And the rope is probably only tied to the horse, right?//

He could probably take a crack at the other ones, too. He was fairly certain he knew how many flowers there were, and that the math was wrong in the last question entirely and the dollar wasn't missing, so much as mislead.

"Nicely done," Miss Bennet said warmly. "Some of these problems rely on preconceptions. The assumption that a horse's rope would be tied to a fixed point, which isn't said, or that the name pattern would continue -- which asks you to overlook that you've already been given the last child's name. Misdirection."

Jonothon nodded a little, and then shrugged.

//I think th'last one is misdirection, too. The dollar isn't missing at all. The math adds up perfectly until the question itself asks where the math went wrong.//

"Right again," she beamed. "It's taking the twenty-seven dollars that the men paid and then adding, to that, the two dollars the bellboy has ... which is misguided, since the two dollars was part of the twenty-seven to start. The three dollars to make thirty has already been dispersed back to the lodgers."

Awww, yeah. What Jonothon lacked in looks, he so made up in logic.

Kinda. He was still scratching his head a little at the jelly donut one.

//I could probably work my way through the rest of them. I imagine that a few of them are misleading, too, but I'd need a bit of time to poke at them some, first.//

"I'm quite willing to offer assistance," she said kindly. "Some of them really are as straightforward as they seem, but it requires analyzing the problem to find the most efficient answer."

Jono nearly cracked a smile, at that. As best as he could, at any rate.

//Three flowers, then. A rose, a tulip, and a daisy. I'm not entirely certain how I ought to go about solving the donut one, really. I haven't figured out how the scale figures in, or if it figures in at all.//

Rose Hathaway

"Three flowers precisely," she laughed. "The scale is key. If you could have as many weighings as you liked, you would have no difficulty finding the donut -- four would do it. Divide the eight into four sets of two, and for each pair, weigh one against each other. When you have one outweighing its counterpart, that's the one hiding a ring."

Rose might have been paying more attention if she hadn't been eyeing the two babies with her suspiciously.

They weren't crying. Something weird was happening.

//Right. But yer can only use the scale twice,// Jono pointed out. //I suppose I might start by dividing the eight into two sets of four, and then divide the four that are heavier into two more sets of two, but...//

He shrugged a little.

//It still leaves some to be measured. And that's really only assuming that all the doughnuts weigh exactly the same, and that th'jelly's been measured in kind, as well. Which is sort of ridiculous in reality, as I think doughnuts are divvied out by size, not technically by weight, but for the sake of the riddle I'll accept it.//

Edited 2009-11-20 00:49 (UTC)

Miss Bennet was not expecting children, in her class, but she gave Rose a sympathetic smile nonetheless.

"Are ... you all right?" she asked, delicately.

That wasn't entirely what she meant, but it seemed a nice opening.

Spock

"Professor Skywalker is a sadist," Rose informed Miss Bennet.

Spock was, indeed, present. As he had already discerned the answers to all of the logic problems, he chose to remain silent during the discussion and let the other students figure them out. He believed this to be a logical decision.

Aravis

Zayne Carrick

Upon closer inspection, it seemed the children weren't children, but were rather dolls. She laughed.

"Am I to presume this is some strange class assignment, then?"

"Is the other end of the rope tied to anything?" Zayne asked. "If it's not, the horse could wander around all it wants."

"We're supposed to watch them for two weeks," she said, making a face. "But this is the first time they've stopped crying since I got 'em this morning."

Yuffie Kisaragi

Yuffie was taking notes, and actually writing the answers to most of them, with one hand, and holding a bottle for the cranky robot baby to drink.

"Here's a small hint, then," she said. "Leaving some to be measured isn't necessarily a problem, if you can deduce, by elimination, that the ring lies in the unmeasured set, and work from there."

"Perhaps they enjoy logic riddles," Miss Bennet teased. "You should keep a small book of them handy, and read them out when the little ones start to fuss."

Calvin

"No, it isn't," Miss Bennet smiled. "Nicely done. That riddle simply allows the one who hears it to add his or her own preconceptions to the question, and make it far more difficult that it sounds on its face."

Miss Bennet smiled, kindly, at Yuffie. "Shall I presume that you are also in Master Skywalker's class?"

"Does that really work?" Rose asked hopefully. "I don't know anything about babies at all."

"I doubt it," she laughed. "But I'm afraid I shan't be much help myself. I have younger sisters, but they aren't so much younger than myself as to be pertinent to this discussion. I wish you luck, as I expect you'll need it."

After a moment's consideration, she added, "Though perhaps ... your would-be children are soothed by the sound of the lecture, which suggests you might find a book to read in a low, calming tone. Or perhaps it means my class does function as a sedative."

Penelope Wilhern

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