You have a dark room containing two tables. On one table, there are 100 coins, with 80 showing heads and 20 showing tails. The other has nothing on it. You cannot see the coins, nor feel which side is up. How can you get the same number of coins tails up on both tables with at least one coin on each?
Stastically you dump all of the coins on the floor and then take any arbitrary number from 1 to 50 and put an equal number on each table. But then stastics lie.
I would move the two tables exactly next to each other and place all of the coins on the junction of the tables so that they were on both tables. Guaranteed to work, independent of how many coins you pocket...
I love math logic stuff. A tough one. This is classic partitioning.
Take 20 coins off of the table and move them to the other table, flipping them over in the process. Without going into all the details of the logic involved in a formula, if you happen to pick only one of the coins that was already tails, that table would have one less tails coin (19) but the table with just 20 coins would then have 19 tails coins. If you happened to pick just 2 tails coins, then the original table would have 18 and the new table 18. And so on.
I take any number of coins and put them into two piles, one pile on each table, but each coin in each pile is standing on edge. I guarantee that there are an equal number of heads and tails in each pile on each table.