r**********i
发帖数: 25 | 1 the cafeteria has 360 roses to sell for valentine's day, you want to pick
out a perfect red rose for someone special. when you get to the cafeteria,
you discover:
-every third rose is too short
-every fourth rose has too many thorns
-every fifth rose is wilted
-every sixth rose is pink
-every eighth rose is yellow
if these are the only problems that the roses have, how many perfect roses
are there for you to choose from?
show all work.
昨天朋友小孩的作业，非常感谢，我自己做的是144，不知道对不对. |
n***p
发帖数: 7668 | 2 Yes.
【在 r**********i 的大作中提到】
: the cafeteria has 360 roses to sell for valentine's day, you want to pick
: out a perfect red rose for someone special. when you get to the cafeteria,
: you discover:
: -every third rose is too short
: -every fourth rose has too many thorns
: -every fifth rose is wilted
: -every sixth rose is pink
: -every eighth rose is yellow
: if these are the only problems that the roses have, how many perfect roses
: are there for you to choose from?
|
n*****n
发帖数: 3123 | |
s***g
发帖数: 495 | 4 维恩图法。
【在 r**********i 的大作中提到】
: the cafeteria has 360 roses to sell for valentine's day, you want to pick
: out a perfect red rose for someone special. when you get to the cafeteria,
: you discover:
: -every third rose is too short
: -every fourth rose has too many thorns
: -every fifth rose is wilted
: -every sixth rose is pink
: -every eighth rose is yellow
: if these are the only problems that the roses have, how many perfect roses
: are there for you to choose from?
|
w*******y
发帖数: 372 | 5 Non-perfect ones:
360/3 + 360/4 + 360/5 - 360/12 - 360/15 - 360/20 + 2 * (360/60) = 222
So it's 138.
Welcome to throw bricks.
【在 r**********i 的大作中提到】
: the cafeteria has 360 roses to sell for valentine's day, you want to pick
: out a perfect red rose for someone special. when you get to the cafeteria,
: you discover:
: -every third rose is too short
: -every fourth rose has too many thorns
: -every fifth rose is wilted
: -every sixth rose is pink
: -every eighth rose is yellow
: if these are the only problems that the roses have, how many perfect roses
: are there for you to choose from?
|
p***0
发帖数: 20 | 6 360*2/3*3/4*4/5*5/6*7/8=105 |
r**********i
发帖数: 25 | 7 我的算法大概是这样：八的倍数已经包含在四的倍数里。六的倍数包含在三的倍数里。
所以要算的就是三百六十里有多少是三四五的倍数。三的倍数是360/3.四的倍数是360
／4.五的倍数是360／5.
360／5+360／3+360／4就是282
然后减去共同倍数重叠部分。
四和五共用倍数360／20 就是18
三和五共同倍数360／15就是24
四和三共同倍数360／12就是30
三者和是72
最后加上三四五共同倍数360／60 就是6。因为三者重叠部分被加了三次又减三次最后
没包含在内。
好的玫瑰是216.不好的是360-216就是144. 谢谢高人原来小学的图有名字叫维恩图法。 |
p***0
发帖数: 20 | 8 Do a correction:
360*2/3=240 not too short
240*3/4=180 not too short and not too many thorns
180*4/5=144 not too short and not too many thorns and not wilted
Among this
144*1/6 = 24 pink
144*1/8=18 yellow
So good rose number is
144-24-18=102
The first three and color are independent.
The color pink/yellow can not on the same rose. |
w*******y
发帖数: 372 | 9 Why "最后加上三四五共同倍数"?
Your answer is correct. But I think the reasoning is more complicated, as
follows:
Let S3 denote the number of roses with weakness 3 ONLY; so as S4, S5;
Let S34 denote the number of roses with weakness 3&4 ONLY; so as S45, S35;
Let S345 denote the number of roses with weakness 3&4&5 ONLY.
Number of roses with weakness = S3 + S4 +S5 + S34 + S35 + S45 + S345
S345 = 360/(3*4*5)
S45 = 360/(4*5) - S345
...
S3 = 360/3 - S34 - S35 - S345
...
Putting them together, we have
360/3 + 360/4 + 360/5 - 360/(3*4) - 360/(3*5) - 360/(4*5) + 360/(3*4*5) =
216.
The reasoning is more complicated than expected because number such as 360/3
just means the number of roses with AT LEAST weakness 3.
大牛们，is there more intuitive and simplified way to reason?
360
【在 r**********i 的大作中提到】
: 我的算法大概是这样：八的倍数已经包含在四的倍数里。六的倍数包含在三的倍数里。
: 所以要算的就是三百六十里有多少是三四五的倍数。三的倍数是360/3.四的倍数是360
: ／4.五的倍数是360／5.
: 360／5+360／3+360／4就是282
: 然后减去共同倍数重叠部分。
: 四和五共用倍数360／20 就是18
: 三和五共同倍数360／15就是24
: 四和三共同倍数360／12就是30
: 三者和是72
: 最后加上三四五共同倍数360／60 就是6。因为三者重叠部分被加了三次又减三次最后
|
w*******y
发帖数: 372 | 10 The issue of this reasoning is: if you consider in the 240 roses without
weakness 3 (too short), the assumption "every fourth rose has too many
thorns" may not be true anymore.
【在 p***0 的大作中提到】
: 360*2/3*3/4*4/5*5/6*7/8=105
|
|
|
r**********i
发帖数: 25 | 11 谢谢p2010说的很对。粉色玫瑰与黄色玫瑰不可能有交集。我做的时候忽略了。这个是
纽约市十一岁小孩学校的作业题。几个大人做的结果都不同老师还没公布答案所以帮小
孩问问。是不是对十一岁太难了。不是说美国学校数学教育很差。到时比较切合实际生
活是二月十四日的作业。 |
w*******y
发帖数: 372 | 12 the pink and yellow conditions are conflicting each other: at position 48,
what color is the rose? Last condition could be: every 8th is not red.
But that doesn't matter. pink/yellow is still covered by the first two
conditions.
【在 r**********i 的大作中提到】
: 谢谢p2010说的很对。粉色玫瑰与黄色玫瑰不可能有交集。我做的时候忽略了。这个是
: 纽约市十一岁小孩学校的作业题。几个大人做的结果都不同老师还没公布答案所以帮小
: 孩问问。是不是对十一岁太难了。不是说美国学校数学教育很差。到时比较切合实际生
: 活是二月十四日的作业。
|
w*******y
发帖数: 372 | 13 p2010's answer 360*2/3*3/4*4/5 = 144 is an elegant one.
【在 w*******y 的大作中提到】
: the pink and yellow conditions are conflicting each other: at position 48,
: what color is the rose? Last condition could be: every 8th is not red.
: But that doesn't matter. pink/yellow is still covered by the first two
: conditions.
|
b*******n
发帖数: 5065 | 14
这是大学课程里的吧？ 可能属于讨论作业，主要开启思路。
combinatorics。
【在 r**********i 的大作中提到】
: the cafeteria has 360 roses to sell for valentine's day, you want to pick
: out a perfect red rose for someone special. when you get to the cafeteria,
: you discover:
: -every third rose is too short
: -every fourth rose has too many thorns
: -every fifth rose is wilted
: -every sixth rose is pink
: -every eighth rose is yellow
: if these are the only problems that the roses have, how many perfect roses
: are there for you to choose from?
|
r****f
发帖数: 672 | 15 考点：
前三种是独立因素，可重叠
后两种不是独立因素，不可重叠
所以答案是
360*(1-1/6-1/8)*2/3*3/4*4/5=102
看了回帖
居然只有一人答对
可见我们中国人的数学真差
【在 r**********i 的大作中提到】
: the cafeteria has 360 roses to sell for valentine's day, you want to pick
: out a perfect red rose for someone special. when you get to the cafeteria,
: you discover:
: -every third rose is too short
: -every fourth rose has too many thorns
: -every fifth rose is wilted
: -every sixth rose is pink
: -every eighth rose is yellow
: if these are the only problems that the roses have, how many perfect roses
: are there for you to choose from?
|
i*****s
发帖数: 265 | 16 I agree with you: 102
【在 r****f 的大作中提到】
: 考点：
: 前三种是独立因素，可重叠
: 后两种不是独立因素，不可重叠
: 所以答案是
: 360*(1-1/6-1/8)*2/3*3/4*4/5=102
: 看了回帖
: 居然只有一人答对
: 可见我们中国人的数学真差
|
n***p
发帖数: 7668 | 17 你把含前三种缺陷的花挑出来之后,后两种已经自动淘汰了,那是冗余信息
(而且自相矛盾,就像前面有人说的,第24朵花是什么颜色?)
另外,假定只有24朵花,你的答案是多少?自己画24个圈,看看,很容易的穷举.
【在 r****f 的大作中提到】
: 考点：
: 前三种是独立因素，可重叠
: 后两种不是独立因素，不可重叠
: 所以答案是
: 360*(1-1/6-1/8)*2/3*3/4*4/5=102
: 看了回帖
: 居然只有一人答对
: 可见我们中国人的数学真差
|
w*******y
发帖数: 372 | 18 这跟中国有毛的关系么？兄弟，去gym锻炼锻炼，别闷坏了。
【在 r****f 的大作中提到】
: 考点：
: 前三种是独立因素，可重叠
: 后两种不是独立因素，不可重叠
: 所以答案是
: 360*(1-1/6-1/8)*2/3*3/4*4/5=102
: 看了回帖
: 居然只有一人答对
: 可见我们中国人的数学真差
|
K**e
发帖数: 53 | 19 博士, 答案验证过么?
【在 r****f 的大作中提到】
: 考点：
: 前三种是独立因素，可重叠
: 后两种不是独立因素，不可重叠
: 所以答案是
: 360*(1-1/6-1/8)*2/3*3/4*4/5=102
: 看了回帖
: 居然只有一人答对
: 可见我们中国人的数学真差
|
r**********i
发帖数: 25 | 20 今天老师说答案是144 (前几天不是休息今天才有老师的课) |
I*******y
发帖数: 4893 | 21 您的娃可以开心地告诉老师出错题啦
【在 r**********i 的大作中提到】
: 今天老师说答案是144 (前几天不是休息今天才有老师的课)
|
