Question 58
A nine-digit number $\overline{abcdefxyz}$ was written on the board. Bat split it into three-digit blocks $abc,def,xyz$ and combined them arbitrarily into nine-digit numbers. (The source gives $\overline{abcdefabc}$ as an example.) Looking at these numbers, Tsedeg said: “All these numbers give the same remainder when divided by 27.” Is Tsedeg right?