Copyright © University of Cambridge. All rights reserved.
'Watch Your Feet' printed from https://nrich.maths.org/
We received some fantastic solutions to
this Bernard's Bag investigation. One of these came from Adam, from
Milton Mount School. Children at Summercroft Junior School who go
to the lunchtime Challenge Club sent us some very interesting work:
Laura B and Adam sent this diagram showing the longest possible
route for a path 3 paving stones wide and 14 long:
Along with Laura S, Eleanor and Oliver, the
pupils at the club have taken the investigation further and begun
to generalise. They have found a way to work out the number of
"steps" in the longest possible route.
Laura S and Eleanor explain:
We found the longest route by taking the length (L), the amount of
starting places there were (P) and then took (PxL) - (P-l) = The
longest possible route.
Oliver, Laura S and Eleanor extended this
to a path 4 paving stones wide:
Laura S and Eleanor point out that "there
are variations on this, which are just as long". Oliver says that
he worked this out using
(PxL)-(P-2)
Perhaps you'd like to look into these
patterns further.