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Your crazy uncle has built a panic room in his basement. The panic room can only be accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ..., 6 and is 8 digits long. Because your uncle really is crazy, the numeric code must be monotone, meaning either always non-decreasing or always non-increasing. How many possible codes are there under these conditions? Your Answer: Answer

Your crazy uncle has built a panic room in his basement. The panic room can only be accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ..., 6 and is 8 digits long. Because your uncle really is crazy, the numeric code must be monotone, meaning either always non-decreasing or always non-increasing. How many possible codes are there under these conditions? Your Answer: Answer

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Discrete mathematics 

Your crazy uncle has built a panic room in his basement. The panic room can only be accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ... , 6 and is 8 digits long. Because your uncle really is crazy, the numeric code must be monotone, meaning either always non-decreasing or always non-increasing. How many possible codes are there under these conditions? Your Answer: Answer Hide hint for Question 13 For example, using only the digits 0, 1, 2, 3: a 7-digit non-increasing code might be 3322210, or a 9-digit non-decreasing code might be 001123333. Each example could be represented by a bar/star chart, where the stars represent using a particular digit and the bars represent the transitions from one digit to the next. Count the number of bar/star charts for possible non-increasing and possible non-decreasing codes, then use the addition principle.
Transcribed Image Text:Your crazy uncle has built a panic room in his basement. The panic room can only be accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ... , 6 and is 8 digits long. Because your uncle really is crazy, the numeric code must be monotone, meaning either always non-decreasing or always non-increasing. How many possible codes are there under these conditions? Your Answer: Answer Hide hint for Question 13 For example, using only the digits 0, 1, 2, 3: a 7-digit non-increasing code might be 3322210, or a 9-digit non-decreasing code might be 001123333. Each example could be represented by a bar/star chart, where the stars represent using a particular digit and the bars represent the transitions from one digit to the next. Count the number of bar/star charts for possible non-increasing and possible non-decreasing codes, then use the addition principle.
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