Solving nice yet trivial USAMO Problems
by yugrey, May 17, 2011, 3:03 AM
The last USAMO problem from an old one that I solved in a great way:
If you want to try the problem yourself:
Prove that in a deck of n cards with 3 aces, the expected place number of the second ace (you draw from top to bottom) is (n+1)/2.
Nice and easy, but a USAMO #5 in the days when there were only 5 problems on USAMO.
Link to my edit (and solution): http://www.artofproblemsolving.com/Wiki/index.php?title=1975_USAMO_Problems%2FProblem_5&diff=38550&oldid=32557
By the way, we did this one in WOOT, but we used Solution 1. I came up with Solution 2 (there is a chance that maybe someone elsesaid the idea but as far as I can recall I just came up with Solution 2 in one to two minutes after seeing the problem again a acouple days ago).
Anyway, it is nice, elegant, and better than Solution 1.
By the way, AoPS wiki is full of stubs and needs to really be expanded since it is an awesome resource.
If you want to try the problem yourself:
Prove that in a deck of n cards with 3 aces, the expected place number of the second ace (you draw from top to bottom) is (n+1)/2.
Nice and easy, but a USAMO #5 in the days when there were only 5 problems on USAMO.
Link to my edit (and solution): http://www.artofproblemsolving.com/Wiki/index.php?title=1975_USAMO_Problems%2FProblem_5&diff=38550&oldid=32557
By the way, we did this one in WOOT, but we used Solution 1. I came up with Solution 2 (there is a chance that maybe someone elsesaid the idea but as far as I can recall I just came up with Solution 2 in one to two minutes after seeing the problem again a acouple days ago).
Anyway, it is nice, elegant, and better than Solution 1.
By the way, AoPS wiki is full of stubs and needs to really be expanded since it is an awesome resource.
This post has been edited 2 times. Last edited by yugrey, May 17, 2011, 3:05 AM
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