Question 29
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,
$6\quad4\quad2\quad1\quad3\quad5$
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?
$6\quad4\quad2\quad1\quad3\quad5$
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?