Question

What is the number of positive integers less than or equal to 2017 that have at least one pair of adjacent?

Answer 1

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Answer 2

Answer:

738

Step By Step Explaination:

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

Hence, the answer is 738.