Ones, Twos and Threes
Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?
Age
11 to 14
Challenge level
Problem
Each digit of a positive integer is $1$, $2$ or $3$. Each of these digits occurs at least twice in the number.
What is the smallest such integer that is not divisible by $2$ or $3$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 1112233
Digits include $1, 2, 3, 1, 2, 3$ and maybe more
$1+2+3=6$ so any number with digits $1, 2, 3, 1, 2, 3$ is a multiple of $3$
$\Rightarrow$ use another $1$
$1112233$ smallest possible with another $1$ and this is also odd