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, 642135
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?

997

Step-by-step explanation:

odd + odd + odd = odd

odd + even + even = odd

There are 500 odd numbers and 500 even numbers.

Write the numbers in the following order:

odd, even, even, odd, even, even...

odd, even, even, odd, odd...

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250 (odd, even, even) 250 odd

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Hence, the number of odd-sum triples is 748 + 248 + 1 = 997

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong