21-110: Problem Solving in Recreational Mathematics, spring 2010

Calendar

The calendar describes what we did each day and has links to all of the various documents (homework assignments, handouts, and so forth). For a broad overview of the kinds of things we might cover in this course, please see the list of potential topics.

Course documents and handouts

• Syllabus (PDF, TeX)
• First-day questionnaire (PDF, TeX)
• Polyominoes
• Working systematically
• Symmetry and tilings
• Algebra puzzles (PDF, TeX)
• Finding a formula for a sequence of numbers
• Additional topics in number theory
• The extended Euclidean algorithm
• Spring break puzzles (PDF, TeX; MetaPost drawings: Xs on a chessboard, grid sums)
• Sets
• Counting (PDF, TeX)
• Algorithms to find a low-cost Hamiltonian circuit in a weighted complete graph (PDF, TeX).
• Conflict graphs

Homework assignments

• Homework assignment 1 (PDF, TeX): assigned Wednesday, January 13; due Wednesday, January 20.
  • Solutions: PDF, TeX; MetaPost drawings: cube, star, tepee, tetrahedron.
• Homework assignment 2 (PDF, TeX): assigned Monday, January 25; due Wednesday, February 3 (note the change).
  • Solutions: PDF, source files.
• Homework assignment 3 (PDF, TeX; MetaPost drawings: one point, two points, three points, four points, five points): assigned Friday, February 5; due Wednesday, February 17 (note the change).
  • Hints for problem 7: It may be helpful to find a formula for a sequence of numbers; when n = 10, the number of regions is 256 (you can use this to check your formula); be sure to draw your points so that no three chords intersect in a single point.
  • Solutions: PDF, source files.
• Homework assignment 4 (PDF, TeX; MetaPost drawing: sheep pen): assigned Friday, February 19; due Friday, February 26 (though turning it in on Monday, March 1 is fine).
  • Solutions: PDF, TeX; MetaPost drawing: sheep pen.
• Homework assignment 5 (PDF, TeX): assigned Monday, March 15; due Wednesday, March 24.
  • Solutions: PDF, source files.
• Homework assignment 6 (PDF, TeX; MetaPost drawings: streets, chords): assigned Friday, March 26; due Monday, April 5.
  • Solutions: PDF, TeX; MetaPost drawings: streets, chords, square.
• Homework assignment 7 (PDF, TeX): assigned Monday, April 5; due Wednesday, April 14.
  • Solutions: PDF, source files.
• Homework assignment 8 (PDF, TeX; Paraguay, United States; MetaPost drawing: multigraph): assigned Wednesday, April 14; due Monday, April 26.
  • Solutions: PDF, source files.
• Homework assignment 9 (PDF, TeX): assigned Wednesday, April 14; due Friday, April 30.

Project

The project was assigned on Wednesday, March 17. It is due on the last day of class. See the project handout for more details. If you would like to do something other than (or in addition to) the suggestions in the handout, please come talk to me. When you have decided on a project group, please e-mail me to let me know.

• Project handout: PDF, TeX.

Challenge questions

• Friday, February 5: PDF, TeX.

Feedback

I am always interested to get feedback about this course: questions, comments, complaints, and suggestions. You are certainly welcome to talk to me directly. Otherwise, you can e-mail me, deliver a note for me to the Mathematical Sciences department office in Wean Hall 6113, or slip a note under my office door (PPB 342; make sure you mark the note with my name, since I have several officemates).