格拉迪斯（Gladys）写下了四个数字。 这些数字的平均数（平均值）是 13，中位数是 12，众数是 10。 求这四个数字。 答案 ...

1. Use the mode to identify repeated numbers and set up the ordered list.

Since the mode is $10$, the number $10$ must occur more often than any other number.

For four numbers in ascending order, take the first two numbers as
$10,\ 10,\ a,\ b$
where $a \geq 10$ and $b \geq a$.

2. Use the median of four numbers to find the third number.

For four numbers, the median is the mean of the two middle numbers.

So
$\frac{10+a}{2}=12$
$10+a=24$
$a=14$

3. Use the mean to find the fourth number.

The mean is $13$, so the total of the four numbers is
$4\times 13=52$

Hence
$10+10+14+b=52$
$34+b=52$
$b=18$