01204211/homework5 counting 2 - ประวัติรุ่นแก้ไข

Jittat เมื่อ 01:35, 4 ตุลาคม 2558

2015-10-04T01:35:57Z

Jittat เมื่อ 01:31, 4 ตุลาคม 2558

2015-10-04T01:31:02Z

Jittat เมื่อ 01:30, 4 ตุลาคม 2558

2015-10-04T01:30:06Z

Jittat เมื่อ 01:26, 4 ตุลาคม 2558

2015-10-04T01:26:48Z

Jittat เมื่อ 01:25, 4 ตุลาคม 2558

2015-10-04T01:25:39Z

Jittat เมื่อ 01:24, 4 ตุลาคม 2558

2015-10-04T01:24:45Z

Jittat เมื่อ 01:19, 4 ตุลาคม 2558

2015-10-04T01:19:37Z

Jittat เมื่อ 00:51, 4 ตุลาคม 2558

2015-10-04T00:51:04Z

Jittat เมื่อ 00:46, 4 ตุลาคม 2558

2015-10-04T00:46:04Z

Jittat เมื่อ 00:41, 4 ตุลาคม 2558

2015-10-04T00:41:51Z

@@ แถว 3: / แถว 3: @@
 '''Due:''' ''19 Oct 2015''
-'''H.1'''
+'''H.1''' I have 2 pairs of blue socks, 3 pairs of red socks, and 4 pairs of white socks.
 '''H.2''' How many anagrams can you make from the word INNOVATION?
 '''H.3''' How many sorted lists of integer of length <math>k</math> consisting only integers from <math>1</math> to <math>n</math> are there?  (Note that each integer can appear many times in the list. For example, when <math>k=2</math> and <math>n=3</math>, there are 6 of them (i.e.: 1,1; 2,2; 3,3; 1,2; 1,3; and 2,3)).
 '''H.4''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?
 '''H.5''' (LPV-3.6.3) Prove the following identity:
@@ แถว 19: / แถว 27: @@
 </math>
 </center>
 '''H.6''' (LPV-3.8.8) Prove the following identity
@@ แถว 27: / แถว 36: @@
 </math>
 </center>
 '''H.7''' In a village, there are <math>n</math> houses built along a single road.  They plan to plant gardens in front of the houses; therefore they have to choose a set of houses to host the gardens.  Since they do not want to plant too many gardens, they do not want to have two gardens on consecutive houses.  In how many ways can they choose a set of houses such that no two consecutive houses are in the set?  (It is possible that, in the end, they do not plant any garden at all.)
@@ แถว 39: / แถว 49: @@
   o * o
   o o *
 '''H.8'''  You want to tile a walk way of length <math>n</math>.  The width of the walk way is 1 unit.  You have tiles of size 1x1, 2x1 and 3x1.  In how many ways can you do that?

@@ แถว 7: / แถว 7: @@
 '''H.2''' How many anagrams can you make from the word INNOVATION?
-'''H.3''' How many sorted lists of integer of length <math>k</math> consisting only integers from <math>1</math> to <math>n</math> are there?  (For example, when <math>k=2</math> and <math>n=3</math>, there are 6 of them (i.e.: 1,1; 2,2; 3,3; 1,2; 1,3; and 2,3)).
+'''H.3''' How many sorted lists of integer of length <math>k</math> consisting only integers from <math>1</math> to <math>n</math> are there?  (Note that each integer can appear many times in the list. For example, when <math>k=2</math> and <math>n=3</math>, there are 6 of them (i.e.: 1,1; 2,2; 3,3; 1,2; 1,3; and 2,3)).
 '''H.4''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 01:30, 4 ตุลาคม 2558
แถว 40:		แถว 40:
	o o *		o o *

−	'''H.8'''	+	'''H.8''' You want to tile a walk way of length <math>n</math>. The width of the walk way is 1 unit. You have tiles of size 1x1, 2x1 and 3x1. In how many ways can you do that?
		+
		+	Let <math>W_n</math> be the number of ways you can tile the walk way of length <math>n</math> with these tiles.
		+
		+	(a) Specify the recurrence for <math>W_n</math>.
		+
		+	(b) Find the explicit form of <math>W_n</math>. (The details for the Fibonacci sequence will be available on the slide soon.)

@@ แถว 28: / แถว 28: @@
 </center>
-'''H.7''' In a village, there are <math>n</math> hourses built along a single road.  They plan to plant gardens in front of the hourses; therefore they have to choose a set of hourses to host the gardens.  Since they do not want to plant too many gardens, they do not want to have two gardens on consecutive hourses.  In how many ways can they choose a set of houses such that no two consecutive houses are in the set?  (It is possible that, in the end, they do not plant any garden at all.)
+'''H.7''' In a village, there are <math>n</math> houses built along a single road.  They plan to plant gardens in front of the houses; therefore they have to choose a set of houses to host the gardens.  Since they do not want to plant too many gardens, they do not want to have two gardens on consecutive houses.  In how many ways can they choose a set of houses such that no two consecutive houses are in the set?  (It is possible that, in the end, they do not plant any garden at all.)
-For example, if we have 3 houses these are the 5 ways to choose houses.  (* is chosen; o is not)
+For example, if we have 3 houses these are the 5 ways to choose houses.  (* is chosen; o is not)  The first example does not choose any houses.
 2 3
@@ แถว 39: / แถว 39: @@
   o * o
   o o *

@@ แถว 30: / แถว 30: @@
 '''H.7''' In a village, there are <math>n</math> hourses built along a single road.  They plan to plant gardens in front of the hourses; therefore they have to choose a set of hourses to host the gardens.  Since they do not want to plant too many gardens, they do not want to have two gardens on consecutive hourses.  In how many ways can they choose a set of houses such that no two consecutive houses are in the set?  (It is possible that, in the end, they do not plant any garden at all.)
-For example, if we have 3 houses these are the ways
+For example, if we have 3 houses these are the 5 ways to choose houses.  (* is chosen; o is not)
   o o o
   * o o

@@ แถว 7: / แถว 7: @@
 '''H.2''' How many anagrams can you make from the word INNOVATION?
-'''H.3''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?
+'''H.3''' How many sorted lists of integer of length <math>k</math> consisting only integers from <math>1</math> to <math>n</math> are there?  (For example, when <math>k=2</math> and <math>n=3</math>, there are 6 of them (i.e.: 1,1; 2,2; 3,3; 1,2; 1,3; and 2,3).
-'''H.4''' (LPV-3.6.3) Prove the following identity:
+'''H.4''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?
 <center>

@@ แถว 1: / แถว 1: @@
 : ''This is part of [[01204211-58]]''
 '''H.1''' How many anagrams can you make from the word INNOVATION?
@@ แถว 5: / แถว 7: @@
 '''H.2'''
-'''H.2''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?
+'''H.3''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 00:41, 4 ตุลาคม 2558
แถว 1:		แถว 1:
	: ''This is part of [[01204211-58]]''		: ''This is part of [[01204211-58]]''

−	'''H.1'''	+	'''H.1''' How many anagrams can you make from the word INNOVATION?
		+
		+	'''H.2'''
		+
		+	'''H.2''' (LPV-3.4.1) In how many ways can you distribute all <math>n</math> pennies to <math>k</math> children if each child is supposed to get at least 2?