Assorted puzzles

Blasting an asteroid into pieces ●○○○○ 10 ptsBruce the Astronaut must destroy a large asteroid. When he blasts a large asteroid, it splits into two medium asteroids. When he blasts a medium asteroid, it splits into three small asteroids. When he blasts a small asteroid, it vanishes. How many blasts does he need to make the asteroid completely vanish?
Asteroid collisions in a million years ●○○○○ 10 ptsAsteroids with a diameter of at least 1 km collide with the Earth at a rate of approximately 2 per million years. Assume collisions occur according to a Poisson process. What is the probability that in a randomly selected million-year period there is exactly one collision? Round to four decimal places.
Orders of breaking clay targets ●●○○○ 20 ptsEight clay targets are arranged in three hanging columns: two columns of three targets each and one column of two targets. A marksman breaks all the targets by these rules: 1. The marksman first chooses a column from which a target is to be broken. 2. The marksman must then break the lowest remaining target in the chosen column. If the rules are followed, in how many different orders can the eight targets be broken?
Per-pass speed loss in aerobraking ●●○○○ 20 ptsA spacecraft approaches a planet at 18000 m/s and must slow to 8000 m/s over exactly 50 orbital passes. On each pass it keeps the same fraction of its speed. What percentage of its speed must it lose on each pass? Round to two decimal places.

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