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How many positive, five-digit integers contain the three-digit block “123”? Two such integers are 12,350 and 41,232.

 Nov 5, 2019
 #1
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123  in the first through third positions,   we have  (00 - 99) in the last two positions  =  100 integers

 

123  in the second position through fourth positions,  we have  (1 - 9)  in the first position and  ( 0-9)  in the last position

So   9  * 10  =  90 integers

 

123 in the last three positions we have  (1 - 9)  in the first position and  (0 - 9)  in the second position

So  9 * 10  =  90 integers

 

So

 

100 + 90  + 90   =

 

280  integers

 

 

cool cool cool

 Nov 5, 2019
edited by CPhill  Nov 6, 2019
 #2
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CPhill; The inadvertent typo of 180 should read 280.

 Nov 6, 2019
 #3
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THX, guest  !!

 

Corrected  !!!!

 

 

 

cool cool cool

CPhill  Nov 6, 2019

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