These days, in my child’s extracurricular math study group, the teacher no longer sends geometry, combinatorics, number theory, or application questions, but instead sends series questions every day.
The teacher turned the good learning atmosphere into a brain teaser, and I dare not say anything, so I can only complain here. Of course, it is a technical complaint.
Today's number sequence problem is to find out what the next number is after 2, 2, 0, 7, 9, 9.
We hide the standard answers and ideas. Please read them after you finish reading this article:
Many years ago, there was a book that was popular for a while. The title of the book was "The Bible Code". The content roughly said that after observing one by one, it was found that many events were predicted in the Bible. The form was on a certain page of the Bible. Through vertical, diagonal, jumping, and individual letters counted in order by some unknown rules, they were put together in order, which were the names of people and places of certain historical events. If you are interested, you can check out the "Basic Overview of the Bible Code" of OSGeo China Center (https://www.osgeo.cn/post/11250). I won't go into details here. But one thing is clear - a random sequence of sufficient length is very likely to get a shorter sequence you want (this will depend on how Gdel ruins mathematics, so I won't go into details).
So, I am going to find a "simple rule" that can generate a random number sequence to "guess" the next item of any brain teaser sequence. The most handy language at hand is the scripting language python.
First, I calculated the first 12 digits of the trigonometric function tan value from 1 to 1000, and counted the numbers 0 to 9 on each digit, and found that the probability of occurrence is basically the same, which basically meets the distribution requirements.
Then I need a tool that can detect whether the sequence meets the requirements, so I use a state machine to implement it. _state ostensibly counts the length of the existing sequence that meets the overall sequence. In fact, when the value is equal to the standard sequence length, it means that a sequence has been found.
If you are testing genes and other sequences, you should consider issues such as simultaneous detection, but I just want to find a result, so I can tolerate simplifying it.
In the end, the python class was written like this:
class sq_auto_m():
_seq=[]
_full_flag= 0
_stat =0
_count=0
_success=[]
def __init__(self, seq):
self._seq=seq[::]
self.clean()
def init(self,seq):
self.__init__()
def show_seq(self):
print self._seq
def show_cnt(self):
print self._count
def show_suc(self):
return self._success
def clean(self):
self._full_flag= len(self._seq)
self._stat =0
self._count=0
self._success=[]
def push(self,val):
self._count=self._count+1
if self._seq[self._stat]==val:
self._stat=self._stat+1
if self._stat==self._full_flag:
self._success.append(self._count)
self._stat =0
return True
else:
self._stat =0
if self._seq[self._stat]==val:
self._stat=self._stat+1
#print self._stat
if self._stat==self._full_flag:
self._success.append(self._count)
self._stat =0
return True
return False
When executing, call it like this:
r=range(12)
qc=[ sq_auto_m([2,2,0,7,9,9]) for x in r]
i=1
while i< (1<<20):
print i
s=repr(abs(math.tan(i))).replace('.','')
_=[ qc[x].push(int(s[x:x+1])) for x in r]
i=i+1
for x in r:
print x,qc[x].show_suc()
2 to the power of 20 is more than one million. I looked at the output and got impatient after 121516. I forced the termination by pressing Ctrl+C and found that two results had been thrown.
0 []
1 []
2 []
3 []
4 [115141]
5 []
6 [46758]
7 []
8 []
9 []
10 []
11 []
The 6th one was discovered relatively early, appearing at more than 40,000. Print it out and take a look:
>>> for x in range(46753,46759+1):
... repr(abs(math.tan(x)))[:15]
...
'0.1839028578233'
'1.0677023796878'
'3.9603504373298'
'0.3352375585022'
'0.8029491564140'
'9.4218595015405'
'0.5017617686735'
The sixth digit (not counting the decimal point) is 2, 2, 0, 7, 9, 9, 1, so the answer is 1?
This is obviously different from the correct answer, but it also fully illustrates that there is no real environment to test the number series problem, it is just a brain teaser.
This content is originally created by nemon , a user of EEWORLD forum. If you want to reprint or use it for commercial purposes, you need to obtain the author's consent and indicate the source
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