8. Dwarf and river crossing In a land of dwarfs, a mysterious dwarf decides to visit
three of her friends. She carries seven (7) mangoes in
her sack. To reach her first friend she has to cross a
magic river. After she crosses the river, the number of
mangoes in her sack doubles. She then gives her first
friend a number of mangoes. She continues her journey
and then crosses the second magic river. The number of
mangoes doubles again. She gives her second friend the
same number of mangoes. She crosses the third magic
river. Again the number of mangoes doubles. She visits
her third friend and gives the same number again. This
time there are no mangoes left. What number did she
give to each friend?
Investigate with different start numbers. What numbers
work out neatly?​