Vincent and Zane had 82 marbles in total. Zane had 16 marbles more than Vincent at first. After Vincent and Zane played a game with Shiyun, Vincent had ¹₃ as many marbles as Zane. If Vincent lost as many marbles as Zane to Shiyun, find the number of marbles that Vincent lost to Shiyun.

	Vincent	Zane	Difference
Before	1 u	1 u + 16	16
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of marbles at first
= 1 u + 1 u + 16 
= 2 u + 16

2 u + 16 = 82
2 u = 82 - 16
2 u = 66

1 u = 66 ÷ 2 = 33

Since Vincent lost the same number of marbles as Zane, the difference in the number of marbles between Vincent and Zane at first and in the end remains the same.

Difference in the number of marbles in the end
= 3 p - 1 p
= 2 p

2 p = 16

1 p = 16 ÷ 2 = 8

Number of marbles that Vincent lost to Shiyun
= 1 u - 1 p
= 33 - 1 x 8
= 33 - 8
= 25

Answer(s): 25