Prison Cell Problem

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?

Prison Door

1

Prison Door

2

Prison Door

3

Prison Door

4

Prison Door

5

Prison Door

6

Prison Door

7

Prison Door

8

Prison Door

9

Prison Door

10

Prison Door

11

Prison Door

12

Prison Door

13

Prison Door

14

Prison Door

15

Prison Door

16

Prison Door

17

Prison Door

18

Prison Door

19

Prison Door

20

Prison Door

21

Prison Door

22

Prison Door

23

Prison Door

24

Prison Door

25

Prison Door

26

Prison Door

27

Prison Door

28

Prison Door

29

Prison Door

30

Prison Door

31

Prison Door

32

Prison Door

33

Prison Door

34

Prison Door

35

Prison Door

36

Prison Door

37

Prison Door

38

Prison Door

39

Prison Door

40

Prison Door

41

Prison Door

42

Prison Door

43

Prison Door

44

Prison Door

45

Prison Door

46

Prison Door

47

Prison Door

48

Prison Door

49

Prison Door

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.

 

Recently Updated

Circle Equations

Circle Equations

Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle. So far this activity has been accessed 72 times and it is ready for you to enjoy!

Prison Cell Problem

Can 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.

Apple

©1997-2017 WWW.TRANSUM.ORG