Math Question 1

1. There are 5 Bookson the shelves numbered 1-19 , and 5 of them How many of these are not adjacent to this number?

Practice: Insert 5 books into the middle of other books, so that the book will have a a void, so

2, with two colors to dye into a circle of 6 pieces, if by rotation to get is only one, ask a total of how many ____ species dyeing mode

Solution: Two colors, one of the default colors, then n (0) =n (6) =1,N (1) =n (5) =1,N (2) =n (4) =3, N (3) =4 Total - species

3, the calculation expression x6+4x4+2x3+x+1 minimum need to do () multiplication.

Solution: The original can be changed to x3 (x3+x+x+x+x+2) +x+1. which X3 The calculation requires two multiplication. Then x3 and parentheses are multiplied. Total 3 times.

4, if the string s=software, the number of its substring is ()

Solution: The substring of software can range from 1 letters to 8 letters , but with the same alphabetical order, the number of substrings is 8+7+6+5+4 +3+2+1=36. Empty strings are substrings of any string, so 36+1=37.

5, looking for a job season immediately arrived, many students to the library to borrow "interview Treasure" this book, now outside the library has 6 students lined up, of which 3 students to the hands of the "interview treasure" also to the library, there 3 students hope from the library can borrow "interview treasure", if the current library has no inventory "interview treasure", to ensure that the borrowing 3 The classmate can borrow the book, ask this 6 how many kinds of queuing methods are there ()

6, you have a 3X3X3 cube. You are now on the top left vertex, which needs to be moved to the lower right vertex of the back of the diagonal. Each move is not limited to distance, but only from front to back, from left to right, from top to bottom, that is, it is not allowed to skew or back. How many ways are there ?

Solution: This problem can be seen as 3X3X3 Matrix,xyz axis each walk 3 step Ah, from (3,3 ,3) walk to (0,0,0), Altogether there are:= 1680

7, a valid expression is surrounded by () ,() can be nested and connected, such as (()) () is also a legal expression; now there are 6 the (), they can be composed of the number of legal expressions is ____

Solution: Again a Cattleya series .... That's a real hassle to explain.

We can think of the left parenthesis as1, the closing parenthesis is considered0, the combination of these parentheses is onthe arrangement. Here, you need to satisfy any successive subsequence that starts with the first number,0not more than the number of1, that is, the number of closing parentheses is not more than the number of left parenthesis. Assuming that we do not consider this restriction, then all the onSort TotalC(2n,n) species, which is half0Half1We are now looking for ways to get rid of the number of non-conforming requirements. In any sequence that does not meet the criteria, find out what makes0the number exceeds1the number of the first0the position, and then in causing and including this0part of the sequence, to1instead of all0and to0on behalf of all1. As a result, the total sequence becomes a(n+1)a1and the(n-1)a0the sequence. And the process is reversible, meaning that any one has(n+1)a1and the(n-1)a0a sequence that does not conform to a condition, so the number of non-conforming sequences isC(2n,n-1)

So the number of legal permutations is C(2n,n)-C(2n,n-1) = C (12,6)-C (12,5) =132

8. Thevillage chief took 4 pairs of father and son to attend the second leg of the third quarter of a village shot. The village in order to protect children not to be abducted by the rule of the year before, that is, when the children can only eat when the child or their parents, then 4 pairs of father and son in the round table on how many kinds of sitting method. ( rotate, everyone faces a change in direction is a new method of sitting ).

Solution: The key to the problem is to locate the child's father can be divided into the following situations (not 3 father guilt, because, the rest of the father will be next to two children, will be abducted one)

4 father Guilt

2 father guilt

Because the rotation will result in the change of the sitting method, so, for the above two cases are as follows

c8 1 * a4 4 * 2 = 384 (4 guilt rotation has " Span style= "font-family: ' Times New Roman ';" >8 4 Span style= "font-family: the song Body;" > Dad permutation Combination, 4

C8 1 * A4 2 =2 father guilt in area A, so the other two must be opposite, in 8 positions to choose a A there are 8 cases of the starting seat , after the election, The father of a area has a 4 2 cases, The other side is the rest of the father)

Add up is 480 species

9, Tanabata festival n Lovers (n>=2) in a circle to hold a bonfire party. The rules of the party are: men and women are the same, and each pair of lovers is in a neighboring position. How many different kinds of circles are there?

Solution: Http://www.nowcoder.com/test/question/done?tid=716116&qid=3435#summary

According to the question set, requires different circles, which means that the circle can be rotated when the difference caused by, can not be counted. N the individual stands a vertical row of the entire arrangement for n! , N The entire arrangement of individual stations in a circle and irrespective of the rotation of the circle is (n-1)! .

Another,n person is actually 2n couples, each group of couples have 2 kinds of stations,N Group has 2^n type of positioning

10, a team has   JAVA  procedure, with   3/4  c++ program, the team will write   at the same time; JAVA  and   c++ ______ man

Solution:4*5 least common multiple , 20* (2/5+3/4-1) = 3

One,

Math Question 1