Use a range of multiplicative strategies when operating on whole numbers
I can apply the strategy to problem solving questions
A prisoner sits in his cell planning his escape. The prisoner is kept in by 5 laser beams, which operate along a corridor. Each laser is switched off at a specific time interval for just long enough to allow a person to walk through. The time between being switched off for each laser is shown below:
- Laser One = every 3 minutes
- Laser Two = every 2 minutes
- Laser Three = every 5 minutes
- Laser Four = every 4 minutes
- Laser Five = every 1 minutes
The guard patrols and checks the prisoner each time all the laser beams are off simultaneously. Because each laser only switches off for a short time the prisoner knows he can only get past one laser at a time. He has to get past the five lasers from 1 to 5 in order. Laser One is at the entrance of the prisoner’s cell and laser Five is at the door to the outside. He also knows that if he spends longer than 4 minutes 12 seconds in the corridor an alarm will go off.
Can the prisoner escape without the alarm in the corridor going off?
Yes and all the lasers turn off 1 hour
If he can escape, how many minutes should he wait before passing Laser One?
He has to wait for 3 minutes
How much time will he have after passing Laser Five before the guard raises the alarm?