What is the number of positive integers less than or equal to 2017 that have at least one pair of adjacent digits that are both even. For example 24,564 are two examples of such numbers while 1276 does not satisfy the required property. ans-738

• Answer:
  
  738
  
  Step-by-step explanation:
  
  What is the number of positive integers less than or equal to 2017 that have at least one pair of adjacent digits that are both even.
  
  Number should be at least 2 digits
  
  2 digits numbers starting & ending with even number
  
  Starting digits 2 , 4 , 6 , 8  Ending digit 0 2 , 4 , 6 , 8
  
  4 * 5 = 20 numbers
  
  3 Digit numbers
  
  its necessary that Middle number is even number
  
  0 2 4 6 8
  
  1st digit even number 2 4 , 6 , 8   & 3rd digit any digit
  
  5 * 4 * 10 = 200
  
  3rd digit even number 0 2 4 6 8  & 1st digit any ( 1 to 9)
  
  = 5 * 5 * 9 = 225
  
  Repeated number here where 1st & 3rd digit even numbers
  
  4 * 5 * 5 = 100 ( to be reduced)
  
  3 Digit numbers = 200 + 225 - 100 = 325
  
  in 4 digit number  1000 to 1999
  
  1100 to 1999 again these 325 numbers  & additional 50 numbers where 2nd digit = 0 (1000 to 1099)
  
  = 325 + 50 = 375 numbers
  
  2000 to 2017  (1st two digits are even)
  
  All 18 numbers    
  
  Total number = 20 + 325 + 375 + 18 = 738
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