l*****y
发帖数: 317 | 1 On a sheet of paper, you have 100 statements written down. the first says, "
at most 0 of these 100 statements are true." the second says, "at most 1 of
these 100 statements are true." ... the nth says, "at most (n-1) of these
100 statements are true. ... the 100th says, "at most 99 of these statements
are true." how many of the statements are true?
大家放松放松，给大脑做个深呼吸^_^ |
R*******s
发帖数: 136 | |
y***n
发帖数: 153 | |
y****e
发帖数: 28 | 4 I think 50 is the correct answer.
Let S_i be the i-th statement, we have
if S_i is correct, then S_{i+1} must be correct for all i
By going forwards from 1 to 50, we can infer none of the statements
S_1, ..., S_{50} can be true.
Since none of the first 50 statements are true, the remaining 50 statements
must be true.
【在 y***n 的大作中提到】
: 1
|
e******0
发帖数: 211 | 5 不错的答案
你是数学系的吗
statements
【在 y****e 的大作中提到】
: I think 50 is the correct answer.
: Let S_i be the i-th statement, we have
: if S_i is correct, then S_{i+1} must be correct for all i
: By going forwards from 1 to 50, we can infer none of the statements
: S_1, ..., S_{50} can be true.
: Since none of the first 50 statements are true, the remaining 50 statements
: must be true.
|
y****e
发帖数: 28 | 6 math for undergraduate and I've already switched my major for at least three
times at this stage and I still haven't decided I should switch to Quant.
【在 e******0 的大作中提到】
: 不错的答案
: 你是数学系的吗
:
: statements
|
e******0
发帖数: 211 | 7 年轻就干吧
three
【在 y****e 的大作中提到】
: math for undergraduate and I've already switched my major for at least three
: times at this stage and I still haven't decided I should switch to Quant.
|
y****e
发帖数: 28 | 8 I have worked for quite a few years and I am probably a little bit old.
Maybe not so, Derman started his Quant career when he was around 40.
【在 e******0 的大作中提到】
: 年轻就干吧
:
: three
|
e******0
发帖数: 211 | 9 follow your heart.
【在 y****e 的大作中提到】
: I have worked for quite a few years and I am probably a little bit old.
: Maybe not so, Derman started his Quant career when he was around 40.
|
o**o
发帖数: 3964 | 10 Why S_i=T => S_{i 1}=T ?
I think the statements can be paired,
First S_1=F and S_{100}=T, both by contradiction,
Then S_2=F and S_{99}=T, then so on.
【在 y****e 的大作中提到】
: I think 50 is the correct answer.
: Let S_i be the i-th statement, we have
: if S_i is correct, then S_{i+1} must be correct for all i
: By going forwards from 1 to 50, we can infer none of the statements
: S_1, ..., S_{50} can be true.
: Since none of the first 50 statements are true, the remaining 50 statements
: must be true.
|
|
|
w******i
发帖数: 503 | |
l*****y
发帖数: 317 | 12 On a sheet of paper, you have 100 statements written down. the first says, "
at most 0 of these 100 statements are true." the second says, "at most 1 of
these 100 statements are true." ... the nth says, "at most (n-1) of these
100 statements are true. ... the 100th says, "at most 99 of these statements
are true." how many of the statements are true?
大家放松放松，给大脑做个深呼吸^_^ |
R*******s
发帖数: 136 | |
y***n
发帖数: 153 | |
y****e
发帖数: 28 | 15 I think 50 is the correct answer.
Let S_i be the i-th statement, we have
if S_i is correct, then S_{i+1} must be correct for all i
By going forwards from 1 to 50, we can infer none of the statements
S_1, ..., S_{50} can be true.
Since none of the first 50 statements are true, the remaining 50 statements
must be true.
【在 y***n 的大作中提到】
: 1
|
e******0
发帖数: 211 | 16 不错的答案
你是数学系的吗
statements
【在 y****e 的大作中提到】
: I think 50 is the correct answer.
: Let S_i be the i-th statement, we have
: if S_i is correct, then S_{i+1} must be correct for all i
: By going forwards from 1 to 50, we can infer none of the statements
: S_1, ..., S_{50} can be true.
: Since none of the first 50 statements are true, the remaining 50 statements
: must be true.
|
y****e
发帖数: 28 | 17 math for undergraduate and I've already switched my major for at least three
times at this stage and I still haven't decided I should switch to Quant.
【在 e******0 的大作中提到】
: 不错的答案
: 你是数学系的吗
:
: statements
|
e******0
发帖数: 211 | 18 年轻就干吧
three
【在 y****e 的大作中提到】
: math for undergraduate and I've already switched my major for at least three
: times at this stage and I still haven't decided I should switch to Quant.
|
y****e
发帖数: 28 | 19 I have worked for quite a few years and I am probably a little bit old.
Maybe not so, Derman started his Quant career when he was around 40.
【在 e******0 的大作中提到】
: 年轻就干吧
:
: three
|
e******0
发帖数: 211 | 20 follow your heart.
【在 y****e 的大作中提到】
: I have worked for quite a few years and I am probably a little bit old.
: Maybe not so, Derman started his Quant career when he was around 40.
|
|
|
o**o
发帖数: 3964 | 21 Why S_i=T => S_{i 1}=T ?
I think the statements can be paired,
First S_1=F and S_{100}=T, both by contradiction,
Then S_2=F and S_{99}=T, then so on.
【在 y****e 的大作中提到】
: I think 50 is the correct answer.
: Let S_i be the i-th statement, we have
: if S_i is correct, then S_{i+1} must be correct for all i
: By going forwards from 1 to 50, we can infer none of the statements
: S_1, ..., S_{50} can be true.
: Since none of the first 50 statements are true, the remaining 50 statements
: must be true.
|
w******i
发帖数: 503 | |
r****t
发帖数: 10904 | 23 这个和哪个系有啥关系，随便哪个系的都能做这题
【在 e******0 的大作中提到】
: 不错的答案
: 你是数学系的吗
:
: statements
|
L**********u
发帖数: 194 | 24 too oooooooooooooooooooooooooooold
"
of
statements
【在 l*****y 的大作中提到】
: On a sheet of paper, you have 100 statements written down. the first says, "
: at most 0 of these 100 statements are true." the second says, "at most 1 of
: these 100 statements are true." ... the nth says, "at most (n-1) of these
: 100 statements are true. ... the 100th says, "at most 99 of these statements
: are true." how many of the statements are true?
: 大家放松放松，给大脑做个深呼吸^_^
|
