Pizza Cut
Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
Problem
Using only six straight cuts, find a way to make as many pieces of pizza as possible.
(The pieces can be different sizes and shapes).
Getting Started
You might find it useful to print off this page of circles which you can draw on and/or cut out.
Student Solutions
Ananta, Rishika and Navya from Suncity School in Haryana, India used an HTML webpage to investigate this. They made a table of all the possibilities, and found that it was possible to make 22 pieces of pizza using 6 cuts:
Take a look at Ananta, Rishika and Navya's full solution to see what their pizzas looked like.
They also found a general formula for the number of pieces of pizza:
For ‘n’ (non-congruent) chords (cuts) we end up getting maximum of $1+T_n$ number of regions where $T_n$ is the $n$th triangular number. Where $T_n$ is given by $T_n=\frac{n(n+1)}{2}$
This is very interesting - I wonder why this happens? It definitely seems to be true for between 1 and 6 cuts, but will it keep being true for larger numbers?
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
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