Cathy, Jane and Pamela each had some beads and decided to play a game with their beads. In round 1, Cathy lost ¹₂ of her beads to Jane. In round 2, Jane lost ¹₂ of her total number of beads to Pamela. In round 3, Pamela lost ¹₂ of her total number of beads to Cathy. In the end, Cathy, Jane and Pamela had 139, 88 and 50 beads respectively. How many beads did Jane have at first?

	Cathy	Jane	Pamela
Before  1	2 b	87
Change 1	- 1 b	+ 1 b
After 1	1 b	176
Before 2	89	2 u
Change 2		- 1 u	+1
After 2		1 u	100
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Cathy, Jane and Pamela in the end	139	88	50

Working backwards.

1 p = 50

At the start of Round 3:
Number of beads that Pamela had
= 2 p
= 2 x 50 
= 100

At the start of Round 2:
Number of beads that Cathy had
= 139 - 1 p
= 139 - 50
= 89

At the end of Round 3:
Number of beads that Jane had = 88

1 u = 88

At the end of Round 1:
Number of beads that Jane had
= 2 u
= 2 x 88 
= 176

1 b = 89 

At the end of Round 1:
Number of beads that Cathy had = 89

At the start of Round 1:
Number of beads that Jane had
= 176 - 1 b
= 176 - 89
= 87

Answer(s): 87