I often have a few books with bookmarks in them at once. I enjoy classics more than contemporary works of fiction, often read historical fiction, and love to get glimpses into other people's lives by reading memoirs and biographies.
I'm spending my vacation reading Diana Wynne Jones books. It's lovely--no thinking required, polishing off a book a day. One of the books was based on the ballad Tam Lin, and I was quite apprehensive about it because I read a different book based on the same ballad, which I couldn't put down but realized I hated after I'd finished it. But this one didn't disappoint me--it more than made up for the other one. DRD
I *just* finished Danica McKellar's _Math Doesn't Suck_. When I first read a review and learned that there was a "math horoscope" and quizzes (not math quizzes, but the kind in magazines), I was a little skeptical. But I have to admit, I really liked it! Danica tackles lots of middle school math concepts and explains them in ways that are fairly easy to understand, and uses creative word problems to make the math concepts come to life. She also includes testimonials from successful women who once struggled in math, and encouraging quotes and passages.
I only have one criticism: it's definitely aimed at straight girly-girls, and the occasional gay boy might really appreciate it too. I was more of a tomboy, so at the age when this book would have been beneficial for me, I probably would have rolled my eyes at a lot of it.
Thanks for the helpful review, Lisa. I didn't see it before I worked with you tonight. And nice job solving Don's math puzzle this evening. Perhaps Don will give us all here a puzzle from the book he's reading, How Would You Move Mount Fuji?
Finishing Harry Potter 3, Fullmetal Alchemist 1 and "The Backwash Squeeze and Other Improbable Feats". OK, here's the puzzle: You have two jars and 100 marbles. Fifty of the marbles are red and 50 are blue. One of the jars will be chosen at random; then 1 marble will be withdrawn from that jar at random. How do you maximize the chance that a red marble will be chosen? (You must place all 100 marbles in the jars.) Answer next Tuesday.
Bonus problem: Why are manhole covers round instead of square?
Cooksin, if the jars are chosen at random there would be a 50/50 chance of red/blue. I'm wondering if this is a trick question and a 50% chance is as good as it gets?
OK, I'm done with lateral thinking and back to math:
Put one red marble in one jar and the remaining 49 in the other jar along with all 50 blue marbles.
There's obviously a 50/50 chance of either jar being chosen. If the jar with the one red marble is chosen the chance of a red is 100%. 50% x 100% = 50%.
If the other jar is chosen, the chance of a red is approx 49.5%. 50% x 49.5 = 24.75%.
Overall, the percentage probability of getting a red is 50% + 24.75% = 74.75%.
This would answer the bonus question also, since this will be the highest percentage of getting a red.
OK, now my brain hurts. Please tell me this is correct or I'm going to lose my marbles.
Darn...I'm just reading all of this for the first time right now. Didn't get a chance to respond. Oh well, *shrug*.
I don't understand the manhole cover one though. Why does a round cover over a round hole have less of a chance of falling in than would a square cover over a square hole? The hole still has to be smaller than the cover. I must be missing something. Oh--the diagonal that would exist with the square cover but not with the circular cover?
Ok, I understand that the round cover would have to have a small lip to keep it from falling in, but would still be round.
But if the "manhole" itself were square, then couldn't the cover be square too? (With the same lip to keep it from falling in?) Or does it boil down to a diagonal being longer than a square's side, while a diameter of a circle is constant? What exactly is the essence of the solution?
Lisa, you can put a square the same size as its hole in the hole if you lift it, turn it on its side and use the diagonal. A circular lid cannot be turned and forced into a hole the same size as itself. Did I describe this correctly, Don?
All this talk of "diagonal" and whatnot is not making sense to me :( My brain is trying to make it make sense, but alas...no. I guess that's why I'm an English major...
Ok, thanks Christine--that's what I was thinking. The circle has a constant diameter while a square's side is smaller than it's diagonal, so it could fall in if turned. I just wanted to make sure that was it.
Of course, if someone wanted to expose the manhole by turning the cover and pushing it through, they could just as easily expose the manhole by lifting it up and running off with it, LOL. You can do that whether it's square or round.
25 comments:
I'm spending my vacation reading Diana Wynne Jones books. It's lovely--no thinking required, polishing off a book a day. One of the books was based on the ballad Tam Lin, and I was quite apprehensive about it because I read a different book based on the same ballad, which I couldn't put down but realized I hated after I'd finished it. But this one didn't disappoint me--it more than made up for the other one. DRD
I *just* finished Danica McKellar's _Math Doesn't Suck_. When I first read a review and learned that there was a "math horoscope" and quizzes (not math quizzes, but the kind in magazines), I was a little skeptical. But I have to admit, I really liked it! Danica tackles lots of middle school math concepts and explains them in ways that are fairly easy to understand, and uses creative word problems to make the math concepts come to life. She also includes testimonials from successful women who once struggled in math, and encouraging quotes and passages.
I only have one criticism: it's definitely aimed at straight girly-girls, and the occasional gay boy might really appreciate it too. I was more of a tomboy, so at the age when this book would have been beneficial for me, I probably would have rolled my eyes at a lot of it.
~Lisa
Thanks for the helpful review, Lisa. I didn't see it before I worked with you tonight. And nice job solving Don's math puzzle this evening. Perhaps Don will give us all here a puzzle from the book he's reading, How Would You Move Mount Fuji?
Finishing Harry Potter 3, Fullmetal Alchemist 1 and "The Backwash Squeeze and Other Improbable Feats".
OK, here's the puzzle:
You have two jars and 100 marbles. Fifty of the marbles are red and 50 are blue. One of the jars will be chosen at random; then 1 marble will be withdrawn from that jar at random. How do you maximize the chance that a red marble will be chosen? (You must place all 100 marbles in the jars.)
Answer next Tuesday.
Bonus problem: Why are manhole covers round instead of square?
Put all the red marbles on top.
Bonus: so the lid can't fall in
I wouldn't have gotten the marble one, but I totally knew the manhole cover one!
Give us another one, Don. And do you like the book they come from?
Sorry, Ins - Not correct. Remember, a marble will be drawn from the jar AT RANDOM.
Nailed the manhole one, tho.
Don, put all the red marbles in one jar, and all the blue ones in the second jar.
Cooksin, if the jars are chosen at random there would be a 50/50 chance of red/blue. I'm wondering if this is a trick question and a 50% chance is as good as it gets?
Got it! Don't put the marbles in the jars until you know which jar has been chosen, then fill it with all red marbles.
Sorry kids, there is a solution tht gets you better odds than 50-50. And yes, you have to load the jars first.
Bonus time- What ARE the best odds you can get?
Darn, you didn't tell me that!
I'm still thinking......
Do all the marbles have to be the same size?
OK, I'm done with lateral thinking and back to math:
Put one red marble in one jar and the remaining 49 in the other jar along with all 50 blue marbles.
There's obviously a 50/50 chance of either jar being chosen. If the jar with the one red marble is chosen the chance of a red is 100%. 50% x 100% = 50%.
If the other jar is chosen, the chance of a red is approx 49.5%. 50% x 49.5 = 24.75%.
Overall, the percentage probability of getting a red is 50% + 24.75% = 74.75%.
This would answer the bonus question also, since this will be the highest percentage of getting a red.
OK, now my brain hurts. Please tell me this is correct or I'm going to lose my marbles.
Darn...I'm just reading all of this for the first time right now. Didn't get a chance to respond. Oh well, *shrug*.
I don't understand the manhole cover one though. Why does a round cover over a round hole have less of a chance of falling in than would a square cover over a square hole? The hole still has to be smaller than the cover. I must be missing something. Oh--the diagonal that would exist with the square cover but not with the circular cover?
~Lisa
100% Correct Ins!
Lisa- the round cover would have to have a small lip to keep it from falling in, but it would still be round.
WHOO-HOO Maybe I'll sleep tonight!
Insomniac, I am impressed! Well done!
Ok, I understand that the round cover would have to have a small lip to keep it from falling in, but would still be round.
But if the "manhole" itself were square, then couldn't the cover be square too? (With the same lip to keep it from falling in?) Or does it boil down to a diagonal being longer than a square's side, while a diameter of a circle is constant? What exactly is the essence of the solution?
Lisa, you can put a square the same size as its hole in the hole if you lift it, turn it on its side and use the diagonal. A circular lid cannot be turned and forced into a hole the same size as itself. Did I describe this correctly, Don?
Absolutely.
All this talk of "diagonal" and whatnot is not making sense to me :( My brain is trying to make it make sense, but alas...no. I guess that's why I'm an English major...
*sigh*
*now hates Danica McKellar*
And I never liked the Wonder Years either :P
Ok, thanks Christine--that's what I was thinking. The circle has a constant diameter while a square's side is smaller than it's diagonal, so it could fall in if turned. I just wanted to make sure that was it.
Of course, if someone wanted to expose the manhole by turning the cover and pushing it through, they could just as easily expose the manhole by lifting it up and running off with it, LOL. You can do that whether it's square or round.
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