Solution: We buy the prize from 2 yuan, the prize from 4 yuan and the prize from 10 yuan (16-a-b).

Then 2a+4b+10 (16-a-b) = 50.

2a+4 b+ 160- 10a- 10b = 50

-8a-6b=- 1 10

-2(4a+3b)=- 1 10

4a+3b=55

b=55-4a/3，

c= 16-a-(55-4a)/3

Simplified c=a/3+7/3

So there are 2 yuan Prize, 4 yuan Prize (55-4a)/3, 10 yuan Prize (a/3+7/3).

I'll also give you the results:

And because at least one of each kind, * * * bought 16 pieces,

It is known that a+b is greater than or equal to 2 and less than or equal to 15.

3(a+b) is greater than or equal to 6 and less than or equal to 45,

A is greater than or equal to 10 and less than or equal to 15.

①a= 10，b=5，c= 1

②a= 13，b= 1，c=2