Gillian, Nicole and Kimberly each had some beads and decided to play a game with their beads. In round 1, Gillian lost ¹₂ of her beads to Nicole. In round 2, Nicole lost ¹₂ of her total number of beads to Kimberly. In round 3, Kimberly lost ¹₂ of her total number of beads to Gillian. In the end, Gillian, Nicole and Kimberly had 119, 99 and 52 beads respectively. How many beads did Nicole have at first?

	Gillian	Nicole	Kimberly
Before  1	2 b	131
Change 1	- 1 b	+ 1 b
After 1	1 b	198
Before 2	67	2 u
Change 2		- 1 u	+1
After 2		1 u	104
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Gillian, Nicole and Kimberly in the end	119	99	52

Working backwards.

1 p = 52

At the start of Round 3:
Number of beads that Kimberly had
= 2 p
= 2 x 52 
= 104

At the start of Round 2:
Number of beads that Gillian had
= 119 - 1 p
= 119 - 52
= 67

At the end of Round 3:
Number of beads that Nicole had = 99

1 u = 99

At the end of Round 1:
Number of beads that Nicole had
= 2 u
= 2 x 99 
= 198

1 b = 67 

At the end of Round 1:
Number of beads that Gillian had = 67

At the start of Round 1:
Number of beads that Nicole had
= 198 - 1 b
= 198 - 67
= 131

Answer(s): 131