Discovered by R.V. Heath in 1950:That didn't make sense to me, so I set up a little spreadsheet to check it, and I included x's and y's to see if it works.
Think of two positive integers.
Add them to get a third number.
Add the second number and the third number to get a fourth number.
Continue in this way until you have 10 numbers.
The sum of the 10 numbers is 11 times the seventh number.
To check it out, click the link above and enter any two integers in the yellow boxes of the top left. The totals show up in the green to the far right.
I'll tell you in advance that it works.