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Question
QUESTION: we have X number of squares, each square can be connected only on a side (no diagonals)thus a square has 4 possilbe connecitons.
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how many different combinations can be created based on the number of squares? Different means that changing the prespective does not make a different combo.(no mirrors etc)
1sq = 1, 2sq=2,3sq=2, 4sq=5 5sq =8
if you cannot solve please recommend where i should look
thank you
ANSWER: There is a worksheet sent with all of the combinations.
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If you have ever played the computer game of Tetris, reflections are definitely different.
For example, with 4 squares, the figure below 2 and the figure to the right of that one are different.
In the spreadsheet, I have the number of squares.
To the left of this number, I have all of the possible combinations.
Note that for 1, 2, or 3 squares, you are right.
Any other combination is just a rotation of one given.
Above the row of combinations that has a 4 to the left,
I have 5 combinations that have a number above.
The ones with no number above are just a reflection of the last one.
Note that the set following 2 and 4 are just the reflection of the last combination.
For the last two rows, they both have all of the combinations of 5 squares.
Numbers 2, 3, 4, and 7 can be reflected. Note that 4 figures can be reflected.
Just for fun I used 6 squares as well. I believe that there are
---------- FOLLOW-UP ----------
QUESTION: we both made a mistake for five there are ten
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ANSWER: I have drawn out more than 10, so there are least that many.
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If reflections are not allowed, I only have 9.
It is difficult with 5 - how can a million be done?
---------- FOLLOW-UP ----------
QUESTION: when i sent you the first question, i said there were 8, you responded with 9 the "stairs"however we both forgot the cross. check the image that i have sent.
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obviously, it would not be possible to draw a million, however it should be possible to create a formula that would make it possible to find the number of non repeating combos.
if you could help with a formula or tell me who you think could help me, i appreciate it.
thanks
So with the cross there is one more.
Like I said, it starts to get messy when there are only 5.
If you have n squares, you'll have to consider all of the rectangles that could hold the figure.
That is, if you put the whole shape in a rectangle, how big would it be?
For 4 squares, there would be 3 rectangles. The first is 1x4, and includes only 1 shape.
The second is 3x2, and includes 3 shapes. The last is a 2x2, and includes 1 shape.
Form this, it can be said there are 5 shapes, as shown.
But for size n, you have to worry about how many choices actually show a connected graph.
It could be done, but would take a very very long time.
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| Comment | thank you for your time and effort. unless i find a formula i will need to write a progrram to do the work. if you have any further ideas please write. jimmydeancooper dot live.com | ||
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