Wow, nice problem!
Light one end of one string and both ends of the other. When the latter string is completely burnt, light the unlit end of the former string. When that string is completely burnt, 45 minutes will have passed.
It isolates voting irregularities to a single state.
The trouble with this argument, as pointed out at http://www.electionmethods.org/college.htm, is that a small irregularity in a single state which changes the result of the election there is magnified by causing all of the state's electors to be changed! Small amounts of voting fraud in a few close elections could completely change the result.
It balances differences in voter turnout.
You're assuming that the people in New York who were prevented from voting would have voted the same way as those that did. If the storm prevents people in one area (who may be likely to all vote for one candidate) from voting, then the fact that their opinion isn't being heard is magnified by giving all the state's electors (instead of, say 30% of the electors) to a candidate selected by the other areas. This artificially raises the national importance of those who were able to vote by giving them more electoral votes/person.
If a state has a large immigrant population, it is important the state's interests are represented in proportion to its size even though many of its residents may be unable to vote.
This cuts both ways. The electoral college does indeed help states with a large perecentage of people who are ineligible to vote. But that only means that the (relatively) small percentage of people in those states who are able to vote are getting more national importance than those in other states (similar to the case above).
The electoral college ensures elections will always have a definite outcome.
The last argument isn't very convincing--an accurate vote that is eventually agreed upon is much better (in my opinion) than a quickly counted vote that is just a guess of what voters want. If the popular vote isn't entirely one-sided, that is all the more reason to be sure that every vote is counted! Of course, the election must be decided before the new president must take office, but I don't see why the electoral college is necessary for that to happen.
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Wow, nice problem! Light one end of one string and both ends of the other. When the latter string is completely burnt, light the unlit end of the former string. When that string is completely burnt, 45 minutes will have passed.