Advent Puzzles 2014: puzzle 7 solution

Advent puzzle 7: use all of 7, 12, 1 and 4, with any of + − × ÷ ( ), to make all totals from 1 to 24. One of these can't be made. Which one?

— Portsmouth MathsJam (@MathsJamPOR) December 7, 2014

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

$1=(12-4-7)\times1$
$2=1+12-4-7$
$3=7-1-(12\div4)$
$4=7-(12\div4\times1)$
$5=7+1-(12\div4)$
$6=12\div(7-1)+4$
$7=(12\times4+1)\div7$
$8=4+12-1-7$
$9=(4+12-7)\times1$
$10=1+4+12-7$
$11=12\div(4-1)+7$
$12=(7-1)\times4-12$
$13 \mbox{ cannot be made.}$
$14=7+12-1-4$
$15=(12-7)\times(4-1)$
$16=1+7+12-4$
$17=(7\times4)+1-12$
$18=(12\div4)\times(7-1)$
$19=(12-7)\times4-1$
$20=(12-7)\times4\times1$
$21=(12-7)\times4+1$
$22=4+7+12-1$
$23=(4+1)\times7-12$
$24=1+4+7+12$