PDA

View Full Version : Intermediate Flight of Stairs

noreply
05-04-2012, 03:49 AM
There are four friends racing together down a flight of stairs. Person A goes 2 steps at a time, Person B goes 3 steps at a time, Person C goes 4 steps at a time and Person D goes 5 steps at a time.

The only steps which all four tread on are the top one and the bottom one.

1. How many stairs in the flight?

2. How many stairs in the flight were stepped on exactly once?

MAS1
05-15-2012, 12:21 PM
There are four friends racing together down a flight of stairs. Person A goes 2 steps at a time, Person B goes 3 steps at a time, Person C goes 4 steps at a time and Person D goes 5 steps at a time.

The only steps which all four tread on are the top one and the bottom one.

1. How many stairs in the flight?

2. How many stairs in the flight were stepped on exactly once?

1.
Person A: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60

Person B: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60

Person C: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

Person D: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

Since the only steps which every person stepped on are 0 (the top) and 60 (the bottom) there are 60 steps in the flight. Of course there could be any multiple of 60 also such as 120, 180, 240, etc. Nice example of Least Common Multiple (LCM).

2. Steps only touched once: 2, 3, 5, 9, 14, 21, 22, 25, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58