Clones
- The definition of clone (See https://en.wikipedia.org/wiki/Clone_(algebra))
- Proof that every clone containing an operation p(y,x,x)=p(x,x,y)=p(y,x,y)=y contains also an operation m(y,x,x)=m(x,y,x)=m(x,x,y)=x. hint: set m(a,b,c) = p(a,p(a,b,c),c))
Grasshopper
- The original problem: http://imo-official.org/problems/IMO2009SL.pdf, C7
- My informal solution that I am trying to follow: http://www.olsak.net/mirek/grasshopper-informal
Lamps
- The original problem: http://imo-official.org/problems/IMO2008SL.pdf, C4