Question 83
A hacker is locked into an underground industrial complex. She is presented with a computer screen, on which appears a long message of length $72$, consisting of the symbols $E$, $X$, $I$, $T$, exactly $18$ letters of each kind in some seemingly random order. The message may be manipulated by inserting any one of the combinations
$EX$, $XE$, $IT$, $TI$, $IXIXI$
at an arbitrary place in the message. Such a combination may also be erased, wherever it may occur in the message.
The hacker may escape when the system is cracked, which happens when only the word `EXIT` is printed on the screen. Show that she may escape using less than $2019$ operations.
$EX$, $XE$, $IT$, $TI$, $IXIXI$
at an arbitrary place in the message. Such a combination may also be erased, wherever it may occur in the message.
The hacker may escape when the system is cracked, which happens when only the word `EXIT` is printed on the screen. Show that she may escape using less than $2019$ operations.