【Question 14】  
The kindergarten teacher distributed 270 apples, 180 pears, and 235 oranges evenly among the children in the senior class, with the remaining apples, pears, and oranges in the ratio of $3: 2: 1$. There are $\qquad$ children in the senior class.
【Analysis and Solution】
Number Theory, Congruence.
If the number of oranges is tripled, the remaining number of oranges will be equal to the remaining number of apples; that is, $235 \times 3=705$ and 270, when divided by the number of children in the senior class, leave the same remainder; the number of children in the senior class is a divisor of $705-270=435$;
If the number of oranges is doubled, the remaining number of oranges will be equal to the remaining number of pears; that is, $235 \times 2=470$ and 180, when divided by the number of children in the senior class, leave the same remainder;
The number of children in the senior class is a divisor of $470-180=290$; thus, the number of children in the senior class is a common divisor of 435 and 290;
$$
(435,290)=5 \times 29=145 \text {; }
$$

The number of children in the senior class is a divisor of 145: $1, 5, 29, 145$;
(1) When there is 1 child in the senior class, $270 \div 1=270,180 \div 1=180,235 \div 1=235$;

0 apples, 0 pears, and 0 oranges remain, which does not meet the problem's conditions;
(2) When there are 5 children in the senior class, $270 \div 5=54,180 \div 5=36,235 \div 5=47$;

0 apples, 0 pears, and 0 oranges remain, which does not meet the problem's conditions;
(3) When there are 29 children in the senior class, $270 \div 29=9 \cdots \cdots .9,180 \div 29=6 \cdots \cdots .6,235 \div 29=8 \cdots \cdots .3$;

9 apples, 6 pears, and 3 oranges remain, $9: 6: 3=3: 2: 1$, which meets the problem's conditions;
(4) When there are 145 children in the senior class, $270 \div 145=1 \cdots \cdots .125,180 \div 145=1 \cdots \cdots 35,235 \div 145=1 \cdots \cdots .90$;

125 apples, 35 pears, and 90 oranges remain, $125: 35: 90 \neq 3: 2: 1$, which does not meet the problem's conditions;
Upon verification, there are 29 children in the senior class.