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Posted on 2016-10-23
Blackboard Sums II
Source: Inspired by Problem Solving 101 by Stephen Muirhead (Chalkdust Magazine)
The numbers 1 to 20 are written on a blackboard. Each turn, you may erase two adjacent numbers, \(a\) and \(b\) (\(a\) is to the left of \(b\)) and write the difference \(a-b\) in their place. You continue until only one number remains.
What is the largest number you can make?
An Arm and a Leg
If 60% of people have lost an eye, 75% an ear, 80% an arm and 85% a leg, what is the least percentage of people that have lost all four?