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 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:


"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? Lexy,
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