A problem by Aryan Gaikwad

Level pending

There are exactly three different pairs of positive integers that add to make six.

1 + 5 = 6 1\quad +\quad 5\quad =\quad 6

2 + 4 = 6 2\quad +\quad 4\quad =\quad 6

3 + 3 = 6 3\quad +\quad 3\quad =\quad 6

How many different pairs of positive integers add to make one-thousand?


The answer is 500.

Aryan Gaikwad by Aryan Gaikwad , 22, India

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2 solutions

Aryan Gaikwad
Mar 27, 2014

By writing the sums as: 1 + 999, 2 + 998, 3 + 997, ... , 499 + 501, 500 + 500. It is clear that the number of different pairs is five hundred.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammed Zain
Mar 28, 2014

1+999 2+998 3+997 . . 500+500 last pairs

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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