Little Pika Can Barely Add
Little Pika who is five and half years old has just learnt addition. However, he does not know how to carry. For example, he can add 14 and 5, but he does not know how to add 14 and 7. How many pairs of consecutive integers between 1000 and 2000 (both 1000 and 2000 included) can Little Pika add?
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The numbers that are eligible can be divided into 4 groups(We are considering the smaller of the 2 consecutive numbers) :-
1 . Numbers whose all the digits following 1 range from 0 to 4 .The number of such possibilities = 5 ∗ 5 ∗ 5 = 1 2 5 .
2 . Numbers whose last digit is 9 ,others range from 0 to 4 ,the number of possibilities = 5 ∗ 5 = 2 5 .
3 . Numbers whose last 2 digits are 9 s and others range from 0 to 4 .The number of possibilities = 5 .
4 . Numbers whose last 3 didits are 9's and there is only one possibility i.e , 1999.So no. of possibilities = 1 .
hence the total number of pairs of consecutive integers is 1 2 5 + 2 5 + 5 + 1 = 1 5 6 .