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Solve This: Char's Secret

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My wife Char and I moved to Colorado from California a few years ago and were immediately enchanted with the change of seasons; so much so that we've developed the habit of trying to guess the outdoor temperatures during the winter. Every night before going to bed we step outside for a few minutes and then we see who can come closest to guessing the temperature to the nearest degree. I lived in Colorado as a teenager and I can usually sense the ballpark temperature by the way my breath condenses and the feelings in my nose and lungs when I breathe. So I usually guess first. Then Char steps out to the front walkway, comes back in, touches the cold door knob, contemplates for a few seconds and makes her guess. Then we both go look at the indoor/outdoor thermometer.

I've begun to realize over the years that Char gets the right answer about half the time which is a little embarrassing . Why would Char and I have about the same probability of getting the better answer?

Last year we had a particularly prolonged cold spell and Char, comfortable in front of the fireplace reading a book, didn't want to go outside. So I stepped outside, did my usual breath tests, felt the door knob, and looked at the clear Colorado night sky until my nose began to go numb. Coming back in I made my guess, 11 degrees Fahrenheit.

To my surprise, she offers to make a guess also. She puts down her book, closes hers eyes for a moment and says "10 degrees." We both go check the thermometer. And…she's right on! It reads exactly 10 degrees!

The cold spell lasted about a week and each night Char chose to stay inside. But she still guessed the temperature and continued beat me five out of seven days! I asked if she had looked at the thermometer and she laughed and said no.

Finally she told me how she did it and I realized that even if I was a trained meteorologist my odds of beating her wouldn't have been better.

What was her secret?

Winner:

Char's trick is to always allow her husband to guess the temperature first. She then always guesses 1 degree up or down from his guess and this way is (almost) guaranteed a 50% chance of being closer than her husband.

You can see this by taking it to the extreme case where they are guessing temperature to 4 decimal places. In this case it is almost impossible that the initial guess will be correct, all that Char then has to do is pick lower or higher which she can do with 50% success rate on average.

Beating her husband 5/7 times during the cold spell was likely just a run of 'good luck' (not so far away from the 3.5/7 that she ought to have got 'right').--kabdullah

 

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