Computation Workshop Solution Checker

Convex Polygons

Let \(D\) be the set of all lattice points \((x,y)\) in the plane such that both \(x\) and \(y\) are positive integers less than \(10\). We are looking for polygons whose vertices are chosen from \(D\).

Part A How many triangles have all their vertices chosen from \(D\)?
Part B How many convex quadrilaterals have all their vertices chosen from \(D\)?

Alphabetical Integers

The numbers from "one" to "ninety-nine" are written down in two lists. On one list they are written in numerical order: {`one', `two', `three', \(\ldots\) , `ninety-nine'}. On the other list they are written in alphabetical order. Let \(S\) denote the sum of all numbers which are in the same place on both lists.

Part A What is \(S\)?
Part B If "ninety-nine" is replaced by "nine hundred", then what would \(S\) be now?