December 17, 2009

So my final for my problem solving class was to come up with a problem of our own. I couldn't decide on just one, so I made two.

Here they are if anyone wants to take a crack at them, although I don't expect anyone besides Chris to. However, Chris, I told you the answers so you don't get to play.




Problem 1:

Consider a row of 101 urns. Each urn can contain a maximum of 1 ball and has a number on it noting the total number of balls between it and its two neighboring urns. The first two are labeled with the number 2 and the last two are labeled with the number 2. There is only one more urn labeled with the number 2 and all the rest are labeled with the number 1. What is the likeliness that the 48th urn contains a ball?

A. 100%
B. 0%
C. 33%
D. 50%

Problem 2:


Two circles, one situated inside the other, create a ring. A chord of the outer circle, tangent to the inner circle, has length 2sqrt(19). The difference of the two circles’ radii is 1. How many circles, tangent to both the inner and outer circles, can fit inside the ring without overlapping?

A. 56
B. 57
C. 58
D. 59

Active Discussion

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