SDMO posted under Home by George
The San Diego Math Circle held the SDMO today, a few of the problems were interesting. In particular, the last one, dealing with intervals. Let I, I1, I2, ..., In be intervals such that I contains I1 through In. Show the the union of the left halves of intervals I1 through In contains at least half of I. On first looking at this problem, it seemed to shout measure theory at me, and I was almost tempted to start thinking about it in terms of more general metric spaces and using Lebesgue measure. I don't think this should be too hard... some algebra should do the trick I think. Perhaps the intervals could also be generalized to be any desired set. A follow up may come if I get some time to work on this.
| Author | Message |