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a Show that the pattern above can be cleared in 11 steps. b Explain why it is impossible to clear the pattern above in fewer than 11 steps.

a Show that the pattern above can be cleared in 11 steps. b Explain why it is impossible to clear the pattern above in fewer than 11 steps.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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21-11-16 ● ● L- 8 7 6 5 4 3 I 2 1 --> 13 1 A B C D E F G H a Show that the pattern above can be cleared in 11 steps. b Explain why it is impossible to clear the pattern above in fewer than 11 steps. c Explain why the following pattern is not clearable. 8 7 6 5 4 2 1 A B C D E F G H d What is the smallest number of tokens that can appear in a non- clearable pattern? Explain your answer. I 2 I I 6- 29 -> 3 -> 5 -> 9 ----> 8 19 C --> 11 ----> 10 ----> 1
Transcribed Image Text:21-11-16 ● ● L- 8 7 6 5 4 3 I 2 1 --> 13 1 A B C D E F G H a Show that the pattern above can be cleared in 11 steps. b Explain why it is impossible to clear the pattern above in fewer than 11 steps. c Explain why the following pattern is not clearable. 8 7 6 5 4 2 1 A B C D E F G H d What is the smallest number of tokens that can appear in a non- clearable pattern? Explain your answer. I 2 I I 6- 29 -> 3 -> 5 -> 9 ----> 8 19 C --> 11 ----> 10 ----> 1
13 GoGo Tokens are put on some squares of an 8 x 8 grid to make a pattern, such as the one shown in this diagram. 8 7 6 5 4 3 2 1 A B C D E F G H We try to remove the tokens in a sequence of clearing steps. A clearing step consists of choosing a row or a column which contains only 1 or 2 tokens and removing them. For example, we cannot initially remove all tokens from column D. But we can first clear row 5 and then, in some later step, remove the two remaining tokens in column D. If all tokens in a pattern can be removed from the grid using some sequence of allowable steps, then the pattern is called clearable. The above pattern is clearable because we can remove all tokens using the following sequence of 13 allowable steps (among other possibilities): 2, E, 8, G, 7, F, D, 5, 6, 3, 4, A, 1. These 13 steps are represented by arrows numbered 1 to 13 in the fol- lowing diagram. O . P C A C
Transcribed Image Text:13 GoGo Tokens are put on some squares of an 8 x 8 grid to make a pattern, such as the one shown in this diagram. 8 7 6 5 4 3 2 1 A B C D E F G H We try to remove the tokens in a sequence of clearing steps. A clearing step consists of choosing a row or a column which contains only 1 or 2 tokens and removing them. For example, we cannot initially remove all tokens from column D. But we can first clear row 5 and then, in some later step, remove the two remaining tokens in column D. If all tokens in a pattern can be removed from the grid using some sequence of allowable steps, then the pattern is called clearable. The above pattern is clearable because we can remove all tokens using the following sequence of 13 allowable steps (among other possibilities): 2, E, 8, G, 7, F, D, 5, 6, 3, 4, A, 1. These 13 steps are represented by arrows numbered 1 to 13 in the fol- lowing diagram. O . P C A C
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could you please explain how to do parts c. and d. 

 

13 GoGo Tokens are put on some squares of an 8 x 8 grid to make a pattern, such as the one shown in this diagram. 8 7 6 5 4 3 2 1 A B C D E F G H We try to remove the tokens in a sequence of clearing steps. A clearing step consists of choosing a row or a column which contains only 1 or 2 tokens and removing them. For example, we cannot initially remove all tokens from column D. But we can first clear row 5 and then, in some later step, remove the two remaining tokens in column D. If all tokens in a pattern can be removed from the grid using some sequence of allowable steps, then the pattern is called clearable. The above pattern is clearable because we can remove all tokens using the following sequence of 13 allowable steps (among other possibilities): 2, E, 8, G, 7, F, D, 5, 6, 3, 4, A, 1. These 13 steps are represented by arrows numbered 1 to 13 in the fol- lowing diagram. O . P C A C
Transcribed Image Text:13 GoGo Tokens are put on some squares of an 8 x 8 grid to make a pattern, such as the one shown in this diagram. 8 7 6 5 4 3 2 1 A B C D E F G H We try to remove the tokens in a sequence of clearing steps. A clearing step consists of choosing a row or a column which contains only 1 or 2 tokens and removing them. For example, we cannot initially remove all tokens from column D. But we can first clear row 5 and then, in some later step, remove the two remaining tokens in column D. If all tokens in a pattern can be removed from the grid using some sequence of allowable steps, then the pattern is called clearable. The above pattern is clearable because we can remove all tokens using the following sequence of 13 allowable steps (among other possibilities): 2, E, 8, G, 7, F, D, 5, 6, 3, 4, A, 1. These 13 steps are represented by arrows numbered 1 to 13 in the fol- lowing diagram. O . P C A C
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