Use a range of multiplicative strategies when operating on whole numbers

I can apply the strategy to problem solving questions

The escape

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?

I came to more than one answer it is just about what strategy you used.

- He can't do it because he spends to long in the corridor
- He can't because the guard will come to check on him because he comes when all lasers are off and 3+2=5 and 4+1=5 as well so the guard would come at laser 3.
- He might also be able to get through all and then have 12 seconds to run from the guard (unless guard is fit then he will catch the prisoner unless he has a getaway car waiting.)
- Etc.

If he can escape, how many minutes should he wait before passing Laser One?

None he can go once the first laser has gone because it is right in front of his cell entrance so he can act like he is just standing around until the laser turns off.

How much time will he have after passing Laser Five before the guard raises the alarm?

- He will have 12 seconds to run
- It depends if he even gets to laser five
- It also depends on how long the guard takes.

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