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How many 5-digit positive integers are there using only distinct odd digits, where no two adjacent digits can be more than 6 apart?

 Jul 16, 2020
 #1
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According to my computer, there are 1071 such odd numbers, provided the five odd digits (1, 3, 5, 7, 9) are allowed to repeat such as: 11357, 53379....etc.

 Jul 16, 2020
 #2
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They aren't allowed to repeat.

Guest Jul 17, 2020
 #3
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OK then, with all the following restrictions:

 

1 - That all 5 digits be odd

2 - That they all be distinct or different from each other.

3 - That  no two adjacent digits can be more than 6 apart [I took this to mean that the difference between any two adjacent digits be 6 or less)

4 - If I got all the conditions right, then you have the following numbers:

 

13579 , 13597 , 13759 , 13795 , 13957 , 13975 , 15379 , 15397 , 15739 , 15793 , 15937 , 15973 , 17359 , 17395 , 17539 , 17593 , 17935 , 17953 , 31579 , 31597 , 31759 , 31795 , 35179 , 35971 , 37159 , 37951 , 39517 , 39571 , 39715 , 39751 , 51379 , 51397 , 51739 , 51793 , 53179 , 53971 , 57139 , 57931 , 59317 , 59371 , 59713 , 59731 , 71359 , 71395 , 71539 , 71593 , 73159 , 73951 , 75139 , 75931 , 79315 , 79351 , 79513 , 79531 , 93157 , 93175 , 93517 , 93571 , 93715 , 93751 , 95137 , 95173 , 95317 , 95371 , 95713 , 95731 , 97135 , 97153 , 97315 , 97351 , 97513 , 97531 , Total =  72

 Jul 17, 2020

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