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# The Genes of Gilgamesh

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Age 14 to 16

Challenge Level

If three of my grandparents were French and one Russian then I would be said to be one quarter Russian and three quarters French (RFFF). If half of my great-grandparents were English and half other nationalities then I would be said to be half English (EX)

The king of Sumeria around 2600 BC was a great warrior called Gilgamesh . The tale of Gilgamesh the hero stated that Gilgamesh was "Two Thirds God and One Third Man".

Assuming normal reproductive behaviour between a set of ancestors of type pure G and a set of anscestors of type pure M, could you create an offspring of type two-thirds G and one-third M?

How many generations would it take to create a genetic stock to within 1% of (GGM)?

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?