Explore how maths was used during the Roman Empire to solve a rather gruesome problem.
This problem is
called the Josephus problem ‘in honour of’ a Jewish historian living in the 1st
BCE who wrote about the siege of Yodfat. In his original version the soldiers
draw lots, and he and another soldier survive ‘by the grace of God’.
Mathematicians have taken the idea to generate the version above: the general
solution to this version, in which every other soldier is killed, depends upon
nothing more than pattern-spotting, and knowledge of the powers of the 2. It is
accessible to students from Yr 9 up to Yr 13.
The structure
proposed is intended to give students the maximum chance to investigate and
model the situation ‘freestyle’ – only offering scaffolding if needed (like
proposing the tabulation of the number of participants and the number of the
last person standing, starting with small ‘n’).
