Victoria, Cathy and Marion each had some balls and decided to play a game with their balls. In round 1, Victoria lost ¹₂ of her balls to Cathy. In round 2, Cathy lost ¹₂ of her total number of balls to Marion. In round 3, Marion lost ¹₂ of her total number of balls to Victoria. In the end, Victoria, Cathy and Marion had 127, 92 and 59 balls respectively. How many balls did Cathy have at first?

	Victoria	Cathy	Marion
Before  1	2 b	116
Change 1	- 1 b	+ 1 b
After 1	1 b	184
Before 2	68	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 Victoria, Cathy and Marion in the end	127	92	59

Working backwards.

1 p = 59

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

At the start of Round 2:
Number of balls that Victoria had
= 127 - 1 p
= 127 - 59
= 68

At the end of Round 3:
Number of balls that Cathy had = 92

1 u = 92

At the end of Round 1:
Number of balls that Cathy had
= 2 u
= 2 x 92 
= 184

1 b = 68 

At the end of Round 1:
Number of balls that Victoria had = 68

At the start of Round 1:
Number of balls that Cathy had
= 184 - 1 b
= 184 - 68
= 116

Answer(s): 116