Oliver and Andy had 70 beads in total. Andy had 22 beads more than Oliver at first. After Oliver and Andy played a game with Yen, Oliver had ¹₃ as many beads as Andy. If Oliver lost as many beads as Andy to Yen, find the number of beads that Oliver lost to Yen.

	Oliver	Andy	Difference
Before	1 u	1 u + 22	22
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of beads at first
= 1 u + 1 u + 22 
= 2 u + 22

2 u + 22 = 70
2 u = 70 - 22
2 u = 48

1 u = 48 ÷ 2 = 24

Since Oliver lost the same number of beads as Andy, the difference in the number of beads between Oliver and Andy at first and in the end remains the same.

Difference in the number of beads in the end
= 3 p - 1 p
= 2 p

2 p = 22

1 p = 22 ÷ 2 = 11

Number of beads that Oliver lost to Yen
= 1 u - 1 p
= 24 - 1 x 11
= 24 - 11
= 13

Answer(s): 13