6. Determine all three-digit numbers that, when divided by 7, give a remainder of 3, when divided by 9 give a remainder of 5, and when divided by 12 give a remainder of 8.
6. The smallest number divisible by 7, 9, and 12 is $\mathrm{V}(7,9,12)=252$. ..... 3 POINTS

Since $7-3=4, 9-5=4$, and $12-8=4$, the smallest number that, when divided by 7, leaves a remainder of 3, when divided by 9 leaves a remainder of 5, and when divided by 12 leaves a remainder of 8, is obtained by subtracting 4 from the number 252.

2 POINTS
Thus, this number is 248. ..... 1 POINT
The remaining numbers that satisfy the conditions of the problem are $248+252=500$ and $500+252=752$. 4 POINTS

TOTAL 10 POINTS