2012 LSU Math Contest (2)
8:29 AM
Muhammad Yusuf
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22 Water when freezing (and turning into
ice) enlarges its volume by a factor of 1/10. By what
factor will the volume of ice decrease when it is melted?
23 When Achilles started chasing a turtle
they were 990 yards apart. Achilles covers 10 yards in each second. The turtle
covers 1 yard in 10 seconds. How long will it take Achilles to catch the
turtle?
24 For which natural number n is the distance between the numbers 20+21+22+ . . . +2n and 2012
the smallest?
25 A digital clock has a special button
B. Pushing that button causes the clock to switch to the next exact hour, i.e. it
either moves back 0 to 29 minutes or moves forward from 1 to 30 minutes. If at
10:15 the clock shows 8:20, what is the shortest time needed to set the clock
to the right time by only pushing B, possibly a few times. The clock runs
accurately - doesn’t slow or go fast.
26 Find the area of the shaded region.
27 The numbers, 2a - 2, 2a + 2, and a + 1 are lengths of three sides of a
triangle. What can you say about the number a?
28 A polyhedron has n faces, one of which is a regular pentagon.
What is the minimal possible value of n?
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