1. (10 points) Place table tennis balls in 10 boxes, with the number of balls in each box not less than 11, not 17, and not a multiple of 6, and all numbers must be different. Then, at least $\qquad$ table tennis balls are needed.
【Analysis】Starting from 11, find 10 numbers that are neither multiples of 17 nor multiples of 6, then add them up.
【Solution】Solution: The smallest 10 numbers that meet the conditions are:
$11,13,14,15,16,19,20,21,22,23$;
Therefore, at least $11+13+14+15+16+19+20+21+22+23=174$ (units) are needed.
Answer: At least 174 table tennis balls are needed.
The answer is: 174.