a******u
发帖数: 66 | 1 1。N points lie on a circle. You draw lines connecting all the points to
each other. These lines divide up the
circle into a number of regions. How many regions is this? Assume that the
points are scattered in such a way
as to give the maximum number of regions for that N 。答案我觉得应该是2^(N-
1),但是无法用归纳法证明。。。。
2。You are trying to get to Orlando, which is 800 miles away. You have 2500
apples, and you drive a truck
which can hold a thousand at a time. You have unlimited gas, can take as
many trips as yo |
b********a
发帖数: 5418 | 2 1 N<=5是2^(N-1)，之后不是了。貌似不能归结成一个通式。
http://en.wikipedia.org/wiki/Dividing_a_circle_into_areas
2 骆驼题，中间堆栈 我做答案是526，方法见下面链接，如果我做错还请提醒。
http://www.mitbbs.com/article_t/Quant/31251495.html
3 1，2，4
4 楼主试试吧，我刚看到也不记得答案了，动笔试一下我发现很容易推出答案，虽然我
并没有一个能
够推广的方法，还请其他高人指教。
to
the
2^(N-
2500
as
【在 a******u 的大作中提到】
: 1。N points lie on a circle. You draw lines connecting all the points to
: each other. These lines divide up the
: circle into a number of regions. How many regions is this? Assume that the
: points are scattered in such a way
: as to give the maximum number of regions for that N 。答案我觉得应该是2^(N-
: 1),但是无法用归纳法证明。。。。
: 2。You are trying to get to Orlando, which is 800 miles away. You have 2500
: apples, and you drive a truck
: which can hold a thousand at a time. You have unlimited gas, can take as
: many trips as yo
|
t*******y
发帖数: 637 | 3 4.
6210001000
N-
2500
【在 a******u 的大作中提到】
: 1。N points lie on a circle. You draw lines connecting all the points to
: each other. These lines divide up the
: circle into a number of regions. How many regions is this? Assume that the
: points are scattered in such a way
: as to give the maximum number of regions for that N 。答案我觉得应该是2^(N-
: 1),但是无法用归纳法证明。。。。
: 2。You are trying to get to Orlando, which is 800 miles away. You have 2500
: apples, and you drive a truck
: which can hold a thousand at a time. You have unlimited gas, can take as
: many trips as yo
|
a******u
发帖数: 66 | |
b********a
发帖数: 5418 | 5 貌似是唯一的，思路我只有试。。。。
但是有些可以排除啊，比如一定不会有9，8，7等大的数字在非0的地方。
【在 a******u 的大作中提到】
: 第四题答案唯一么？思路是什么呢？
|
J******d
发帖数: 506 | 6 进第二轮了？
N-
2500
【在 a******u 的大作中提到】
: 1。N points lie on a circle. You draw lines connecting all the points to
: each other. These lines divide up the
: circle into a number of regions. How many regions is this? Assume that the
: points are scattered in such a way
: as to give the maximum number of regions for that N 。答案我觉得应该是2^(N-
: 1),但是无法用归纳法证明。。。。
: 2。You are trying to get to Orlando, which is 800 miles away. You have 2500
: apples, and you drive a truck
: which can hold a thousand at a time. You have unlimited gas, can take as
: many trips as yo
|
a******u
发帖数: 66 | |
t*******y
发帖数: 637 | 8 试出来的
这种题除了试不知道还有没有别的办法
【在 a******u 的大作中提到】
: 第四题答案唯一么？思路是什么呢？
|
S*******g
发帖数: 385 | |
p*****k
发帖数: 318 | 10 (1)
was also asked here:
http://www.mitbbs.com/article_t/Quant/31260101.html
the answer is (n^4-6n^3+23n^2-18n+24)/24
it's a classical example in one of Guy's hilarious paper series:
"the strong law of small numbers"
(4)
see discussion here:
http://www.mitbbs.com/article/Quant/31217059_3.html
later learned that there are similar #s which are basically
fixed points (cycles) of some particular mapping:
http://www.wilmott.com/messageview.cfm?catid=26&threadid=74179
and have been already studied in |
b********a
发帖数: 5418 | 11 大牛！
不过没看懂下面的这个做法，主要是不懂他的表达式。。。
struggler (struggler) 于 (Thu Oct 8 15:07:07 2009, 美东) 提到:
再加一个条件，很快就导出唯一解，6，2，1，1
\sum_{i=0}^{i=9} a_i = 10
\sum_{i=0}^{i=9} i a_i = 10
----这步是i×a_i求和？
steps:
1. a_0 = \sum_{i=2}^{i=9} a_i (i-1)
2. \sum_{i=2,i!=a_0}^{i=9} a_i (i-1) = 1
3. a_0>=6, a_2=1, a_i=0 (for i>2, except for i=a_0)
4. a_0=6, a_1=2, a_2=1, a_6=1, a_i=0 (for i>2, except for i=6)
【在 p*****k 的大作中提到】
: (1)
: was also asked here:
: http://www.mitbbs.com/article_t/Quant/31260101.html
: the answer is (n^4-6n^3+23n^2-18n+24)/24
: it's a classical example in one of Guy's hilarious paper series:
: "the strong law of small numbers"
: (4)
: see discussion here:
: http://www.mitbbs.com/article/Quant/31217059_3.html
: later learned that there are similar #s which are basically
|
a******u
发帖数: 66 | 12 是得，求和，因为10个数字加起来得和是10，第一个等式也是同样得原因。
很赞那个鸟人吃饼干得解法！！同样可以设第一个停得位置是x，第二个停得位置是x＋
y，然后解关于x和y得2个线性方程。 |
