4. When raising the number 4 to different powers, Sasha obtained three numbers, all of which had three different digits. Without calculating the results, Andrey noticed that Sasha had made a mistake. What was his basis for this?
This one wants a proof. Work it on paper, read the official solution, then mark
yourself honestly — the ladder only means something if the record is true.
Official solution
4. Powers of the number 4 can end either in 6 or 4, therefore three powers cannot have three different unit digits.
Source: NuminaMath-1.5,
licensed Apache-2.0.
Statement and solution reproduced as published; topic, difficulty and ordering added
by this site.