(3) Jia writes down the positive integers $1,2, \cdots, 2009$ on the blackboard, then turns his back to the blackboard, and asks Yi to erase some of these numbers and add the remainder when the sum of the erased numbers is divided by 7. After several such operations, only two numbers remain on the blackboard, one of which is a single-digit number. Jia asks Yi: “What is the larger of the two remaining numbers?” Answer: “100.” Then, the single-digit number among the remaining two numbers is
(3) 5 Hint: Since $1+2+\cdots+2009 \equiv 0(\bmod 7)$, the one-digit number $a$ satisfies $100+a \equiv 0(\bmod 7)$, thus $a \equiv 5(\bmod 7)$, i.e., $a=5$.