Harder Pigeonhole Principle Problems (Part 1: Pair of numbers which sum to 12)

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If you take 7 numbers from 1-11, you will always have a pair which sum exactly to 12. There's a bit of intuition to why that's true, but how do you prove it. How do you answer pigeonhole principle questions where the pigeons aren't clearly given in the question, well we'll have to define them ourselves!
  1. Jonathan Kim Sing
  2. mathematics
  3. pigeonhole principle
  4. defining pigeons
  5. extension 1
  6. nsw
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This is such an amazing example of the thinking process with the PHP problems! Thanks!

devnavinmadeswaran
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First things first! Well I just wanted to say that it was an excellent and informative lecture!
Now coming to the question part, it is just bugging me that how come when in case of choosing 6 numbers I still get a pair, which is 6 with itself, and that sums up to 12, aren't 7 numbers the minimum no. of numbers required to have a pair whose sum is 12?
I know it is a bit late to post this question but please help me if you can!!
Kudos!!☺️

pinakibose