[ Divisibility rules for 3 and 9$]

Does the number 1234...500 divide by 9? (In the representation of this number, the numbers from 1 to 500 are written consecutively.)

#
This number is comparable to the sum $1+2+\ldots+500=500 \cdot 501: 2 \equiv 250 \cdot 6=1500 \equiv 6(\bmod 9)$.

## Answer

Does not divide.