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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Harriet sent in this solution. Well done!

She has explained her method in the middle of the grid.


Can you see how she did it?

Is this the only solution using her method?




Early in 2015 we had a solution from Ciaran and Alfie in year 5 at Petts Hill Primary In the U.K.



Thank you for this latest solution and the way it was illustrated.
At the beginning of 2016 we had two more solutions. These came from Collaton St. Mary School

Finley and Charlie sent in the first and Archie, Harrison, Huw and Younes sent in the second one.
 

Thank you very much for these, they're both excellent solutions. They may inspire more to come from elsewhere.

It maybe did inspire others because this email came from st. Patrick's Primary School, Sunderland  

From Year 3 at Saint Patrick's Primary in Sunderland who worked together to find a solution:


1        11        3        10

12                              9

5                                2

7        8        6            4


Lew soon realised that you could switch the middle digits around and the totals wouldn't change e.g. 

1        3        11        10

12                              9

5                                2

7        8        6            4

Then he noticed that this could be done systematically one at a time, for each pair of middle digits to find even more solutions. We call them "switch-its".

Following this, Connie realised that you could also swap whole rows or columns, e.g.



7        8        6            4

12                              9

5                                2

1        11        3        10


Therefore there are many different solutions using the same four numbers in the corners (7, 4, 1 and 10).

Thank you Sunderland for your good work!

Home educated , Finn,  wanted to send in a solution. She attached a picture of her Prison Cells solution. She said....

" I found out that you need either one odd number and three even numbers, or one even number and three odd numbers on each side. Realising that made me find the answer rather fast"
4 9 7 5
12     11
6     1
3 10 2 8

Thank you Finn