Sunday Afternoon Maths LVI
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?
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40% of people still have both eyes, 25% both ears, 20% both arms and 15% both legs. If none of these overlap, they add to 100%. Therefore at least 0% of people have lost all four.
Blackboard sums II
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?
Show answer & extension
Hide answer & extension
Erasing 2 and 3; then the result and 4; then the result and 5 and so on will lead to having \(1\) and \(2-\sum_{i=3}^{20}i\) on the board.
Erasing these will give \(1-2+\sum_{i=3}^{20}i=206\).
Extension
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 quotient \(a/b\)
in their place. You continue until only one number remains.
What is the largest number you can make?
