Making Maths Count
Maths Week Scotland – Stepping Up
It’s Maths Week Scotland 2018 and I’m delighted to launch the first of seven daily puzzles that I’ll be sharing this week. Here’s the first challenge, don’t forget to come back for tomorrow’s challenge and the solution to this one.
Three friends visit a museum and walk up a flight of stairs. Ross goes up one step at a time starting with his left foot on the first step. Elena goes up two steps at a time starting with her left foot on the second step and Tom starts with his left foot on the third step and goes up three steps at a time.
Investigate these questions and explain your answers:
(a) Which is the first step that all three will tread on?
(b) Which is the first step that all three will tread on with their right foot?
(c) Which is the first step that all three will tread on with their left foot?
Solution to: Stepping Up
(c) No solution because Ross steps on odd-numbered steps with his left foot and Elena steps on only even-numbered steps with her left foot.
Ross puts his left foot on steps 1, 3, 5, … and his right foot on steps 2, 4, 6, …
Elena puts her left foot on steps 2, 6, 10, … and her right foot on steps 4, 8, 12, …
Tom puts his left foot on steps 3, 9, 15, … and his right foot on steps 6, 12, 18, …
Come back tomorrow for the next challenge!