Pamela, Olivia and Zoe each had some beads and decided to play a game with their beads. In round 1, Pamela lost ¹₂ of her beads to Olivia. In round 2, Olivia lost ¹₂ of her total number of beads to Zoe. In round 3, Zoe lost ¹₂ of her total number of beads to Pamela. In the end, Pamela, Olivia and Zoe had 121, 100 and 71 beads respectively. How many beads did Olivia have at first?

	Pamela	Olivia	Zoe
Before  1	2 b	150
Change 1	- 1 b	+ 1 b
After 1	1 b	200
Before 2	50	2 u
Change 2		- 1 u	+1
After 2		1 u	142
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Pamela, Olivia and Zoe in the end	121	100	71

Working backwards.

1 p = 71

At the start of Round 3:
Number of beads that Zoe had
= 2 p
= 2 x 71 
= 142

At the start of Round 2:
Number of beads that Pamela had
= 121 - 1 p
= 121 - 71
= 50

At the end of Round 3:
Number of beads that Olivia had = 100

1 u = 100

At the end of Round 1:
Number of beads that Olivia had
= 2 u
= 2 x 100 
= 200

1 b = 50 

At the end of Round 1:
Number of beads that Pamela had = 50

At the start of Round 1:
Number of beads that Olivia had
= 200 - 1 b
= 200 - 50
= 150

Answer(s): 150