Good Will Hunting Problems

Author

Eric W. Weisstein
March 25, 2022

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Problems/GoodWillHuntingProblems.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GoodWillHuntingProblems.html.

©2022 Wolfram Research, Inc. except for portions noted otherwise

Blackboard Problem 1

https://en.wikipedia.org/wiki/Good_Will_Hunting#The_first_blackboard_problem

Blackboard Problem 2

n == 10

GraphicsGrid[Partition[StyleGraphs[#,VertexSize->{"Scaled",.05}]&/@Select[GraphData/@GraphData["Tree",10],FreeQ[2]@*VertexDegree],UpTo[5]],Dividers->All,ImageSize->500]

Horvat

Horváth et al. 2013: https://tmcs.math.unideb.hu/load_doc.php?p=245&t=doc

TextGrid[Table[{k,ToRules@With[{ds=Array[d,10-k]},Reduce[Total[ds]==18-k&&GreaterEqual@@Append[ds,3],ds,PositiveIntegers]]},{k,10}],Dividers->All]

Chromatic number problem

Annotate[GraphData[{"Sun",3}]//StyleGraphs,ImageSize->Small]

GraphData[{"Sun",3},"ChromaticPolynomial"][x]//TraditionalForm