Sudoku Logic III

I noticed an interesting twist of logic in today's Sudoku puzzle that enabled quick solution of the rest of the puzzle.  Here's the situation:

Our focus concerns the contents of F6, but our considerations will lead us to learn what goes in F5, after which the rest of the puzzle is not hard.

A little thought shows that A8-A9 must contain 1 and 6, so A5-A6 must contain 2 and 5.  A slightly more involved sequence--(The 5s in D1 and E9 imply that 5 must go somewhere in F4-F6.  5 is forbidden in G5, so it must go in H4-I4, thus eliminating F4)--shows that either F5 or F6 must contain a 5. Now comes the key point:  F5-F6 cannot have a 2, since if it did both A5-A6 and F5-F6 would hold 2 and 5, and there would be duplicate solutions to the puzzle.  Therefore F6 cannot be a 2.

Now let's try to find what does go in F6.  Looking at row 6, remembering F6 cannot be 2, leads to F6 being 5, 7 or 9.  Now 9 can only go in F6 or F8 in the F column.  So let's try 9 in F8, hoping to eliminate either 5 or 7 from consideration in F6.  A 9 in F8 requires that 7 goes in D8.  But in row 6 the 7 can only go in D6 or F6.  The only remaining possibility is F6.  Thus we have learned that F6 can only be 9 or 7, not 5.  But since either F5 or F6 must be 5, the only possibility is that F5 is a 5.  By studying F6, we have the collateral result that F5=5.

Knowing F5=5,  the puzzle solves easily.  (One possible sequence of deductions is A6=5, A5=2, G5=4, F4=3...)

Gas is Too Cheap

A favorite topic of mine--the low price of gas--was covered by Click and Clack this week.  They came to the same conclusion I did in my first blog post: gas costs represent about 25% of the total cost of operating a vehicle.  That's too little, and here are some reasons why.

• Low gas prices distort decision making, and encourage frivolous driving.  I'm guilty of this.  It takes me a half-dozen trips to the hardware store to complete even the simplest household repair.  But I don't care--the gas adds a trivial cost to the project.  At twice the price, I might try a bit harder to be more efficient.
• Low gas prices discourage efficient public transportation.  The higher the price of gas, the more we are likely to take buses, trains, etc. when we need to move from place to place.  These alternates use dramatically less fuels, per person-mile, than personal automobiles.  All over the U.S., people commute 10, 30, even 50 miles each way to work.  This is wasteful and unnecessary, and a huge human cost in wasted time.
• Wars in the Middle East.  We supposedly fight these wars for various reasons, but do you really think we would care so much about that region of the world were it not for the fact that it contains the largest fraction of the world's petroleum reserves?  It really bothers me that we fight war after war there, sending our young men and women to die (not to mention killing their people along the way) without asking for any sacrifice on the part of us who stay at home.  If we had to pay for our military directly from the gas pump, it might help us reassess whether or not we really need to to do all that fighting and killing.
• Petroleum is the ultimate non-renewable resource.  The time scale for it to be replenished by natural processes is millions of years.  We are going to run out in less than a hundred.

There are other arguments, (economics, pollution, global warming...) for why a massive gas tax would be good for us.  But when it comes right down to it, our current practices encourage a wasteful and destructive style of life that our grandchildren will one day condemn us for.