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. ∞ 7 4 33 ● ● ● ● ● ●● ● ● 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.

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. ∞ 7 4 33 ● ● ● ● ● ●● ● ● 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I need help with part d

00
7
6
12
CT
-> 3
-> 5
--> 9
->8
4
-> 11
3
-> 10
2
-> 1
-> 13
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.
7
6
1.0
5
4
3
2
1
I
●
●
7
●
2
T
-
6 4
•
●
•
1
A B C D E
d What is the smallest number of tokens
clearable pattern? Explain your answer.
●
●●
●
F G H
that can appear in a non-

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.
00
7
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.

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