# Making Maths Count

## Maths Week Scotland – Stepping Up

September 10, 2018 by John Swinney MSP 4 Comments | Category Education

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.

Good luck!

**Stepping Up**

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**

(a) 6

(b) 12

(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!*

Tags: John Swinney, Maths Week

Haven’t got a clue…

a) 6, as 6 is a multiple of 1, 2, and 3.

b) 12, as Ross and Tom step on even numbered steps with their right foot and the 12th step is the first multiple of 3 that Elena steps on with her right foot.

c) It will never happen, as Ross and Tom only step on odd numbers with their left feet but Elena never steps on an odd number.

(a) Ross treads on every step, Elena on every 2nd step, and Tom on every 3rd step. So they all tread on every (1st x 2nd x 3rd) = 6th step. The first such step is the 6th.

(b) Ross’s right foot hits every even (2nd) step, Elena’s every 4th, and Tom’s every 6th. So they all hit every LCM(2nd, 4th, 6th) = 12th step, where LCM = lowest common multiple. The first such step is the 12th.

(c) Ross’s left foot hits every ODD step, and only those, while Elena’s hits only EVEN steps (2nd, 6th, 10th, etc). So they never coincide.

A, 6th step. First step that 1, 2 and 3 all go into.

B, 12th step. Everyone on 6th with left therfore on 12th with right.

C, just realised b is wrong. Might try later once head unexplodes.