Knights and Liars

Anna Burago took the lead on this activity for the 2012 Circle on the Road festival.

AUDIENCE: grades 5 to 7 (4 optional)

PLANNING ABSTRACT: “This is a great math circles topic since it combines
combine high entertaining and educational value. Problems of this type are
exciting for children, at the same time they are a great tool for developing the
culture of mathematical reasoning (stating assumptions and conclusions,
explaining the solution in a clear and logical way, checking all possibilities,
negating , etc….)
There exist plenty of great logical problems for the
beginner math circle students and for more advanced students.
We’ll start the activity by introducing the topic. Next, we’ll guide
the students through a series of problems, starting from the easy ones, and
gradually increasing the level of difficulty.
If time and audience level allows, we’ll finish by
discussing how to work with complex logical statements (we’ll explore AND and OR
connectors), and we will introduce several problems of this type. ”

APPRENTICES: Mary O’Keeffe, Elizabeth Parizh, Ashley Ahlin, Yulan Qing


I have uploaded the initial plan of the lesson to Google Docs.
The link is:

My suggestion is to start from the story (plot line), to continue with a set of simple “Knights and Liars” exercises, and then to present children with several problems.

Please read through the document – both exercises and problems. Any other ideas? Any other topics for the exercises? Any other easy and interesting knights and liars problems that you know?

After some meditation on my “Knight and Liars” sample session, I have realized that it mostly targets students of grades 5-7. However, most of the chances are that our audience will be grades 4-5. Reasons: there are A LOT of 4th and 5th-graders registered for workshop (many more that 6th-graders), and not this many activities for 4th-graders.

Therefore, I modified the session. The problems became easier; this way, they are much better suited for grades 4-5. Also, I suggest to use more props and more theatre (staging the problems) while discussing the problems (hats for knights and liars etc.).
The updated activity is located at:


I think the modifications for the younger audience sounds good. And I like the idea of props to help people keep straight who is who. I have some flowered leis that I was thinking of bringing along to help designate the tourists. They would make for nice visuals too if anyone is taking photos or video.

— Mary

Hats: I was planning to make these types of hats: They are easy to make, and 4 pages taped together make a hat of reasonable size.

— Anna