Question 4
A lucky number is one whose sum of its digits is divisible by $7$. For example, $7$, $25$ and $849$ are lucky numbers. The smallest pair of lucky numbers is $7$ and $16$.
a. Find eight consecutive numbers, of which two are lucky numbers.
b. Find $12$ consecutive numbers, such that none are lucky.
c. Shows that any sequence of $13$ consecutive numbers contains at least one lucky number.
a. Find eight consecutive numbers, of which two are lucky numbers.
b. Find $12$ consecutive numbers, such that none are lucky.
c. Shows that any sequence of $13$ consecutive numbers contains at least one lucky number.