What's the sum of the integers from 1 to 300?

This kind of question is frequently asked and easily solved. 1 + 1000 = 1001 2 + 999 = 1001 3 + 998 = 1001 You can see the developing pattern here. Taking integers in order from the top and bottom of the list allows you to create hundreds of equal sums. The last such sum that can be made is 500 + 5001 = 1001. It is clear that you then have 500 sums, each equal to 1001. 1001 X 500 = 500,500 which is the sum of all the integers combined.