# Computation Workshop Solution Checker

## House Numbers

Ross live's on a road with $$N$$ houses numbered from $$1$$ to $$N$$. Amazingly, the sum of all the house numbers before his house is equal to the sum of all the house numbers after his house. So for example, it is possible that $$N=8$$ if Ross lived in house number $$6$$ because $$1+2+3+4+5 = 7+8$$.

Part A If $$N>10$$, what is the smallest possible value of $$N$$? If $$N>10000$$ what is the smallest possible value of $$N$$? If $$N>10^9$$ what is the smallest possible value of $$N$$?

A Quadrilateral is called "good" if it is convex and it's four sidelengths are $$3$$, $$4$$, $$5$$ and $$6$$ (but not necessarily in that order). Let $$A$$ be the diameter of the smallest circle such that we can fit a good quadrilateral completely inside the circle. Let $$B$$ be the diameter of the largest circle such that we can fit a good quadrilateral completely around the circle.
Part A What are the first $$2$$ digits after the decimal point of $$A$$? What are the first $$8$$ digits after the decimal point of $$B$$?