Lucy, Shiyun and Natalie each had some balls and decided to play a game with their balls. In round 1, Lucy lost ¹₂ of her balls to Shiyun. In round 2, Shiyun lost ¹₂ of her total number of balls to Natalie. In round 3, Natalie lost ¹₂ of her total number of balls to Lucy. In the end, Lucy, Shiyun and Natalie had 125, 90 and 59 balls respectively. How many balls did Shiyun have at first?

	Lucy	Shiyun	Natalie
Before  1	2 b	114
Change 1	- 1 b	+ 1 b
After 1	1 b	180
Before 2	66	2 u
Change 2		- 1 u	+1
After 2		1 u	118
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Lucy, Shiyun and Natalie in the end	125	90	59

Working backwards.

1 p = 59

At the start of Round 3:
Number of balls that Natalie had
= 2 p
= 2 x 59 
= 118

At the start of Round 2:
Number of balls that Lucy had
= 125 - 1 p
= 125 - 59
= 66

At the end of Round 3:
Number of balls that Shiyun had = 90

1 u = 90

At the end of Round 1:
Number of balls that Shiyun had
= 2 u
= 2 x 90 
= 180

1 b = 66 

At the end of Round 1:
Number of balls that Lucy had = 66

At the start of Round 1:
Number of balls that Shiyun had
= 180 - 1 b
= 180 - 66
= 114

Answer(s): 114