Zara, Olivia and Xuan each had some marbles and decided to play a game with their marbles. In round 1, Zara lost ¹₂ of her marbles to Olivia. In round 2, Olivia lost ¹₂ of her total number of marbles to Xuan. In round 3, Xuan lost ¹₂ of her total number of marbles to Zara. In the end, Zara, Olivia and Xuan had 125, 105 and 66 marbles respectively. How many marbles did Olivia have at first?

	Zara	Olivia	Xuan
Before  1	2 b	151
Change 1	- 1 b	+ 1 b
After 1	1 b	210
Before 2	59	2 u
Change 2		- 1 u	+1
After 2		1 u	132
Before 3			2 p
Change 3	+ 1 p		- 1 p
After 3			1 p
Comparing Zara, Olivia and Xuan in the end	125	105	66

Working backwards.

1 p = 66

At the start of Round 3:
Number of marbles that Xuan had
= 2 p
= 2 x 66 
= 132

At the start of Round 2:
Number of marbles that Zara had
= 125 - 1 p
= 125 - 66
= 59

At the end of Round 3:
Number of marbles that Olivia had = 105

1 u = 105

At the end of Round 1:
Number of marbles that Olivia had
= 2 u
= 2 x 105 
= 210

1 b = 59 

At the end of Round 1:
Number of marbles that Zara had = 59

At the start of Round 1:
Number of marbles that Olivia had
= 210 - 1 b
= 210 - 59
= 151

Answer(s): 151