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# Sunday Afternoon Maths LV

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Posted on 2016-10-16

## Blackboard Sums

The numbers 1 to 20 are written on a blackboard. Each turn, you may erase two numbers, $$a$$ and $$b$$ and write the sum $$a+b$$ in their place. You continue until only one number remains.
What is the largest number you can make?
Tags: Numbers

## Two Tangents

Source: Reddit
Find a line which is tangent to the curve $$y=x^4-4x^3$$ at 2 points.

## Powerful Quadratics

Source: nrich
Find all real solutions to
$$(x^2-7x+11)^{(x^2-11x+30)}=1.$$
If you enjoyed these puzzles, check out Sunday Afternoon Maths LX,
puzzles about fractions, or a random puzzle.
© Matthew Scroggs 2017