In Transum prison there are 50 prisoners in cells numbered 1 to 50.
On day 1, the guard turns the key in every lock to open every cell.
On day 2, the guard turns the key in every cell which is a multiple of 2. This locks all the even numbered cells.
On day 3, the guard turns the key in every cell which is a multiple of 3, locking or unlocking them.
On day 4, the guard turns the key in every cell which is a multiple of 4, locking or unlocking them.
This continues for fifty days. The prisoners whose cells are open after the 50th day are set free. Which prisoners will be set free?
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
Click on the cells above to open and close the doors. When you have worked out what the situation will be after 50 days click the 'check' button to see if you are correct.

Prison Cell ProblemCan you work out which prisoners will be set free?The key is turned for each factor in the prison cell number. Does that give you a clue? You can use the grid of cells above to simulate the 50 days of activity or you could think of the problem more analytically. There are many more fascinating maths puzzles on Transum.org:


Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. The solutions to this and other Transum puzzles, exercises and activities are available in this space when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher or parent you can apply for one here. A Transum subscription also gives you access to the 'Class Admin' student management system and opens up adfree access to the Transum website for you and your pupils. 
Lexy,
Tuesday, February 6, 2018
"I have gone through it and it continuously says it is wrong! Am I doing something wrong? I have cells 1,4,9,16,25,36,48 and 49 open... Have I missed any?
[Transum: Well done Lexy for finding all of the answers doors that will be left open but you have included one that should remain locked. The correct answer makes a well known number pattern.]"
Holy Cross Maths, Twitter
Tuesday, November 9, 2021
Holy Cross Maths, Twitter
Tuesday, November 9, 2021