【Solution】Solution: According to the analysis, the three sets of numbers, Jia, Yi, and Bing, all form arithmetic sequences, and their sums must be multiples of 3. The sum of the nine numbers is $1+2+3+\cdots+9=45$, which is also a multiple of 3,

The sum of Bing must be a multiple of 3, and the smallest possible sum for Bing cannot be $6=(1+2+3)$.
Bing must be at least 9, and this is feasible through experimentation. Jia and Yi can be:
$(9,8,7)$ and $(5,4,3)$, respectively, and Bing can be: $(1,2,6)$
The smallest possible sum of the numbers on Bing's cards is: $1+2+6=9$
Therefore, the answer is: 9
3. (8 points) The teacher distributed 9 cards, each with a number from $1 \sim 9$, to three students, Jia, Yi, and Bing, giving each of them 3 cards.
Jia said: The numbers on my three cards form an arithmetic sequence;
Yi said: Mine do too;
Bing said: Only mine do not form an arithmetic sequence.
If what they said is all true, then the smallest possible sum of the numbers on the three cards that Bing holds is