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July 29th, 2017, 01:00 PM   #1
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Arranging numbers

Hi,
So I'm faced with this problem:
I want to form a 5 digit number such that 123 are always consecutive. Eg
51423 or 14253. 1,2 and 3 are always consecutive in these numbers
How many of these numbers are possible.
I tried doing it, but I always end up double counting.
Furthermore, how will I expand it for forming a 6 digit number and so on?
Lanthanide is offline  
 
July 29th, 2017, 01:08 PM   #2
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Choose a place for 4, choose a place for 5. Then fill up the number with 123 in consecutvie order.

So I choose place 1 for 4 to get 4****
I choose place 3 for 5 to get 4*5**
I fill up the rest consecutively 41523

Does that tell you how many there are?
Micrm@ss is offline  
July 29th, 2017, 01:17 PM   #3
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I think I understand the process you are using to fill up the spaces. But how will I use that to get the total number of numbers.
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July 29th, 2017, 02:37 PM   #4
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There are 5 places for a 5. There are 4 places remaining for a 4. That's 20 setups. For each setup there is only one way to get 1,2,3 in order. Net result 20 combinations.
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