Yoko, Tammy and Esther each had some beads and decided to play a game with their beads. In round 1, Yoko lost ¹₂ of her beads to Tammy. In round 2, Tammy lost ¹₂ of her total number of beads to Esther. In round 3, Esther lost ¹₂ of her total number of beads to Yoko. In the end, Yoko, Tammy and Esther had 126, 95 and 50 beads respectively. How many beads did Tammy have at first?

	Yoko	Tammy	Esther
Before  1	2 b	114
Change 1	- 1 b	+ 1 b
After 1	1 b	190
Before 2	76	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 Yoko, Tammy and Esther in the end	126	95	50

Working backwards.

1 p = 50

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

At the start of Round 2:
Number of beads that Yoko had
= 126 - 1 p
= 126 - 50
= 76

At the end of Round 3:
Number of beads that Tammy had = 95

1 u = 95

At the end of Round 1:
Number of beads that Tammy had
= 2 u
= 2 x 95 
= 190

1 b = 76 

At the end of Round 1:
Number of beads that Yoko had = 76

At the start of Round 1:
Number of beads that Tammy had
= 190 - 1 b
= 190 - 76
= 114

Answer(s): 114