## 7. 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 her two seconds for the first one, four seconds for the second, six 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 a total of 10 times less time than putting them on. How many seconds does it take centipede Milica to take off all her shoes?

Result: $\quad \mathbf{2 6 0}$
## Solution.

Since there are 50 left shoes, it takes her 50 seconds to put on all the left ones.

For the 1st right shoe, it takes 2 seconds,

for the 2nd right shoe, it takes 4 seconds,

for the 3rd right shoe, it takes 6 seconds,

for the 4th right shoe, it takes 8 seconds,

...

for the 50th right shoe, it takes $2 \cdot 50=100$ seconds.

For all the right shoes, it takes a total of $2+4+6+\ldots+100=2 \cdot(1+2+3+\ldots+50)$ seconds.

It takes her $50+2550=2600$ seconds to put on the shoes, and $2600: 10=260$ seconds to take them off.