## 1. Centipede

Centipede Milica has exactly a hundred legs, 50 left and 50 right. Every morning she puts on 50 pairs of shoes, first all the left ones, and then all the right ones. It takes her one second to put on each left shoe. But then she gets tired, and it takes her more time for the right shoes. It takes one second for the first right shoe, three seconds for the second, five seconds for the third, and so on, with each subsequent right shoe taking two seconds longer than the previous one. In the evening, when she takes off her shoes, it takes her three times less time in total than it does to put them on. How many seconds does it take centipede Milica to take off all her shoes?

Result: $\quad \mathbf{8 5 0}$
## Solution.

Putting on all the left shoes takes $(50 \cdot 1) \mathrm{s}=50 \mathrm{~s}$.

Putting on all the right shoes takes $(1+3+\cdots+99) \mathrm{s}=(25 \cdot 100) \mathrm{s}=2500 \mathrm{~s}$.

Therefore, for putting on all the left and all the right shoes, it takes, in total, $(50+2500) \mathrm{s}=2550 \mathrm{~s}$.

Taking off the shoes takes her (2550 : 3) s $=850 \mathrm{~s}$.