Question 20
Annie wrote eleven consecutive two-digit numbers in a row:
$$a,a+1,a+2,\ldots,a+10.$$
When she erased three numbers, the average of the original numbers is the same as the average of the remaining numbers. If the three numbers erased by Annie are the $x$-th, $y$-th and $z$-th numbers from left to right, what is the number of all possible ordered triples $(x,y,z)$?
$$a,a+1,a+2,\ldots,a+10.$$
When she erased three numbers, the average of the original numbers is the same as the average of the remaining numbers. If the three numbers erased by Annie are the $x$-th, $y$-th and $z$-th numbers from left to right, what is the number of all possible ordered triples $(x,y,z)$?