A website Maths Puzzle Numerical Ability

a+b+c=1
a^2+b^2+c^2=2
a^3+b^3+c^3=3
then
a^5+b^5+c^5=????

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4 4 4 4 =29
using four 4 create the 29 There are 10 parking spaces numbered from 101 to 110. At least one car is parked in these slots. If cars can be parked only at the consecutively numbered parking slots, how many such arrangements can be made. Consider that only one car can be parked in one parking slot and all cars are identical.