Tulips, tulips, everywhere! There are tulips of every color and size - all arranged on floats for the first Tulip Bowl Parade. There are nine marshals stationed every two blocks alsong the parade route, to help control the crowd. The marshals will meet after the parade to make a report. Because the marshals are not used to their wooden shoes, what is the fewest number of combined blocks they could walk for their meeting?
Suppose the marshals are numbered 1 to 9 and stand like this:
Marshals 1 2 3 4 5 6 7 8 9
Blocks | | | | | | | | | | | | | | | | |
Whatever the answer is, it has to be the same answer as
as if the marshals were arranged this way instead:
Marshals 9 8 7 6 5 4 3 2 1
Blocks | | | | | | | | | | | | | | | | |
There is only one way both arrangements could have the
same answer, and that is if they all walked to where the
middle marshal 5 is standing. So everybody except marshal 5
walks to where marshal 5 is standing, and marshall 5 just
stays where he is.
So:
marshals 9 and 1 each walk 8 blocks to where marshal 5 is standing.
That's 16 blocks for those two marshals.
marshals 8 and 2 each walk 6 blocks to where marshal 5 is standing.
That's 12 blocks for those two marshals.
marshals 7 and 3 each walk 4 blocks to where marshal 5 is standing.
That's 8 blocks for those two marshals.
marshals 6 and 4 each walk 2 blocks to where marshal 5 is standing.
That's 4 blocks for those two marshals.
marshal 5 walks 0 blocks, that is, he stays where he is.
That's 0 blocks for that marshal.
16+12+8+4+0 = 40 blocks total.
Edwin