Question 77
We call positive integers such that monotone numbers
- they are written using at least two digits;
- no digit is zero;
- the figures appear in strictly ascending or strictly descending order.
(For example $127$ and $9742$ are monotone numbers, while $172$, $1224$ and $7320$ are not.)
a. Calculate the sum of all five-digit monotone numbers.
b. Determine how many zeros the least common multiple of all monotone numbers ends in (without constraints on the number of digits).
- they are written using at least two digits;
- no digit is zero;
- the figures appear in strictly ascending or strictly descending order.
(For example $127$ and $9742$ are monotone numbers, while $172$, $1224$ and $7320$ are not.)
a. Calculate the sum of all five-digit monotone numbers.
b. Determine how many zeros the least common multiple of all monotone numbers ends in (without constraints on the number of digits).