MathDB

There are two kinds of creatures living in the flatland of Pentagonia: the Spires (

S

) and the Bones (

B

). They all have the shape of an isosceles triangle: the Spiers have an apical angle of

36^o

and the bones an apical angle of

108^o

. Every year on Great Day of Division (September 11 - the day this Olympiad was held) they divide into pieces: each

S

into two smaller

S

's and a

B

; each

B

in an

S

and a

B

. Over the course of the year they then grow back to adult proportions. In the distant past, the population originated from one

B

-being. Deaths do not occur. Investigate whether the ratio between the number of Spires and the number of Bones will eventually approach a limit value and if so, calculate that limit value.

Problem Statement