In a list of numbers, an odd-sum triple is a group of three numbers in a row that add to an odd number. For instance, if we write the numbers from 1 to 6 in this order, 6 4 2 1 3 5 then there are exactly two odd-sum triples: (4,2,1) and (1,3,5). What is the greatest number of odd-sum triples that can be made by writing the numbers from 1 to 1000 in some order?
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Australian Mathematics Competition 2019 - Junior (2019)
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