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How many positive 4-digit integers contain the digit grouping 73 at least once, or the numbers 7 or 3 once? For instance, 2738 and 7344 are two such integers to include.

 Jan 29, 2022
 #1
avatar+865 
+1

73_ _: 8*8

_ 73 _: 7*8

_ _ 73: 7*8

7373: 1

 

No 7 or 3: 7*8*8*8

 

8*8+7*8+7*8+1+7*8*8*8

 

I am not evaluating that, heavens.

 Jan 29, 2022
 #2
avatar+117100 
+1

**73      9*10-1  =  89

*73*      9*10       = 90

73**      10*10-1  = 99

7373                        1

 

89+90+99+1   =  279 

 Jan 29, 2022

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