Advent Puzzles 2014: puzzle 14 solution

(2/2) Advent puzzle 14: one total can't be made. Which one?

— Portsmouth MathsJam (@MathsJamPOR) December 14, 2014

Most numbers have several solutions. One solution for each possible total is given below.

$1=((12\div4)\times3)-8$
$2=8-3-(12\div4)$
$3=3+4+8-12$
$4=(3\times12)-(4\times8)$
$5=4+12-3-8$
$6=((12+4)\div8)\times3$
$7=12-3-(8\div4)$
$8=(3\times4)-12+8$
$9=((3\times4)\div12)+8$
$10=(4-(8\div12))\times3$
$11=3+4+12-8$
$12=(8-4-3)\times12$
$13=8+12-3-4$
$14=3+8+(12\div4)$
$15=(8-3)\times(12\div4)$
$16=(3\times8)+4-12$
$17=(4\times8)-3-12$
$18=(12-3)\times(8\div4)$
$19=3+8+12-4$
$20=((4-3)\times12)+8$
$21=4+8+12-3$
$22\mbox{ cannot be made.}$
$23=(4\times8)-12+3$
$24=(3\times12)-4-8$