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Partitioning 1-D list into 2-D Matrix


I have a question of how to best select elements from a list and reformat
the list into a 2D matrix. Here is an example:

b=Range[1,20]
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

I would like to arrange the list into a 2D array of the following form:
{{1, 3, 5, 7, 9}, {2, 4, 6, 8, 10}, {11, 13, 15, 17, 19}, {12, 14, 16, 18,
20}}

Then
bb=Partition[Partition[b,2],5] 
 <<...OLE_Obj...>> 
almost does what I want if you view this array in MatrixForm[]. However, I
would have to somehow get rid of the innner brackets. I am not sure how to
do that with Flatten[].

I could use brute force and select the elements as follows:
 <<...OLE_Obj...>> 
 <<...OLE_Obj...>> 

I have a feeling there is a much better way to do this.

Thanks in advance,
Chris



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