$(10$ points$)$ Program the Turing Machine simulator to interchange two strings over

$\{0,1\}$ separated by a #$.$ That is$,$ on input w$1$#w$2,$ program the Turing Machine simu$-$

lator to replace the input with w$2$#w$1$ and then halt by accepting. Example: on input

$010$#$11011$ the simulator should replace the input with $11011$#$010$ and then accept. Re$-$

ject any input not in proper form. $($Why is this Turing Machine abuse?$)$

$(15$ points$)$ A palindrome is a string which reads the same forward as backward. For

a string w $=$ s$1$s$2...$ sn of length n this means si $=$ sn$+1$i$.$ Let us define an antipalidrome

as a string w $=$ s$1$s$2...$ sn for which si $6=$ sn$+1$i$.$ Program the Turing Machine simulator

to accept antipalindromes over $\{0,1\}$ of arbitrary length.

$(15$ points$)$ Program the Turing Machine simulator to recognize strings over $\{0,1\}$

with equal number of $1$s and $0$s