This problem is not difficult. A lot of people got long sequences of WA#22 (as well as I did) because of one very stupid mistake. I hope this test will help to understand this mistake:

10 10 20 10 100 1 2012 10000
1
30 60
Answer: 15000.0000000

Thanks for the test.     I get a different answer (and have WA22) -- 14000.   To  get your answer from my calculations you're either stopping the cart in the tunnel (which should never be necessary I think) or you're getting a different value for the time when the fire passes the end of the tunnel.   I'm not sure where my mistake is.   The cart clearly fully enters the tunnel at time 4, and the back of the fire passes the end of the tunnel at time 9 (the fire does not meet the cart before it fully enters the tunnel).  9-4=5.   Covering 20 m over 5 seconds with initial velocity 10 requires deceleration of a = 2.4, which is 1.4 more than 1, thus 14000.   I'm assuming the front of the cart can't enter the tunnel into the fire...

What's wrong with my reasoning?

Edited by author 01.11.2012 12:30

With deceleration 2.4 after 5 seconds in the tunnel a velocity of the cart will be equal 10 - 2.4*5 = -2.
Oops :)

Haha!   That's funny.    I just used "s = v * t - 1/2 a * t^2" but forgot to check whether  it involved "backing up" :).   Sorry to Soren and Alba for barbecuing you before backing you up into the safety of the tunnel!

I'm sure they'll forgive you. You are not the first who does that ;)

It's very funny that this fact didn't allow to solve the problem anybody who tried to do it during the contest.

Edited by author 02.11.2012 12:14

At long last, AC.    Lots of little details to pay attention to in this one!