Online Course Discussion Forum
Math Challenge I-A Spring 2019 Week 3
A new prison has 100100 inmates in 100100 prison cells, with 100100 guards. All the cells start unlocked. The prison has an electronic locking system that needs the authorization of at least 44 guards to lock the door to a cell. The first guard goes through the prison and authorizes every cell to lock. Then the second guard goes through the prison and authorizes every second cell to lock. The rest of the guards continue in this manner (33rd guard authorizes every third cell, etc.) The process continues for all 100100 guards, after which every prisoner whose cell is left unlocked is free to leave. How many prisoners will be set free?
Hi Amy,
Before getting a hint, please look back at the example problem we did in class about the prisoners and guards. Remember we wrote out some small examples to see if we could notice a pattern and why that pattern occurs.
Try looking at the first 10 prisoners, which are set free? For those set free, which guards authorized to lock their cell?
Let us know if you have more questions, but I want to make sure you've tried a few things first.
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