Expert: Paul Klarreich - 5/1/2006

Question
Find two numbers whose difference is 100 and whose sum is a minimum.

Answer
Hi, Nicole,

You wrote:
Find two numbers whose difference is 100 and whose sum is a minimum.

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You're kidding, of course.  Many years ago, it was popular to make up 'stupid-person' jokes, about how stupid a class of people were.  In our academic department this class of people were the Deans.  (Dean of students, Dean of Academic Affairs, Dean of Administration, etc.)  This particular joke went:

Two Deans decided to play a game.  "What game should we play?" asked the first.  "Let's play a game in which we each pick a number," said the second, "and whoever picks the biggest number wins."

"OK," said the first, "you pick the first number."

The second thought a while and said, "7".

The first Dean thought for a long time, and finally said "You win."

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Now suppose your two numbers are  x and x+100.  You pick the first x.  "7", you said.  Ok, I'll pick 6.  Your sum is 114, and mine is 112.  I win.  (I was never a Dean.)

You want to try again?  You, being pretty smart, realize you could pick a negative number.  You pick -1000.  Your sum is -1900.  OK, I pick -1001.  My sum is -1902, which is smaller than yours, and I win again.  

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Perhaps you wrote the wrong thing.