Lynn, Risa and Rachel each had some beads and decided to play a game with their beads. In round 1, Lynn lost ¹₂ of her beads to Risa. In round 2, Risa lost ¹₂ of her total number of beads to Rachel. In round 3, Rachel lost ¹₂ of her total number of beads to Lynn. In the end, Lynn, Risa and Rachel had 137, 84 and 50 beads respectively. How many beads did Risa have at first?

	Lynn	Risa	Rachel
Before  1	2 b	81
Change 1	- 1 b	+ 1 b
After 1	1 b	168
Before 2	87	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 Lynn, Risa and Rachel in the end	137	84	50

Working backwards.

1 p = 50

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

At the start of Round 2:
Number of beads that Lynn had
= 137 - 1 p
= 137 - 50
= 87

At the end of Round 3:
Number of beads that Risa had = 84

1 u = 84

At the end of Round 1:
Number of beads that Risa had
= 2 u
= 2 x 84 
= 168

1 b = 87 

At the end of Round 1:
Number of beads that Lynn had = 87

At the start of Round 1:
Number of beads that Risa had
= 168 - 1 b
= 168 - 87
= 81

Answer(s): 81