Advent Puzzles 2014: puzzle 24 solution

(2/2) Advent puzzle 24: use any of +−×÷() and exponentiation. You can also concatenate the given digits, so 12, 21, 24 etc. are allowed.

— Portsmouth MathsJam (@MathsJamPOR) December 24, 2014

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

$1=1+2+2-4$
$2=4-1-(2\div2)$
$3=(4-(2\div2))\times1$
$4=1\times4\times(2\div2)$
$5=2\times4-1-2$
$6=12-2-4$
$7=2\times4+1-2$
$8=(2\times2)+(1\times4)$
$9=1+2+2+4$
$10=(2\times4)+(1\times2)$
$11=2\times4+1+2$
$12=2\times4\times(1+2)$
$13=2^{4}-1-2$
$14=(2^{4}-2)\times1$
$15=2\times2\times4-1$
$16=1\times2\times2\times4$
$17=2\times2\times4+1$
$18=2+4+12$
$19=2^{4}+1+2$
$20=42\div2-1$
$21=42\div2\times1$
$22=42\div2+1$
$23=1+24-2$
$24=24\times(2-1)$
$25=2+24-1$
$26=24+(1\times2)$
$27=1+2+24$
$28=2\times12+4$
$29=21+(2\times4)$
$30=42-12$
$31=2^{4}\times2-1$
$32=2^{4}\times1\times2$
$33=2^{4}\times2+1$
$34=2^{(1+4)}+2$
$35=(2+4)^{2}-1$
$36=12+24$
$37=(2+4)^{2}+1$
$38=2\times21-4$
$39=42-1-2$
$40=42-(1\times2)$
$41=1+42-2$
$42=42\times(2-1)$
$43=2+42-1$
$44=42+(1\times2)$
$45=1+2+42$
$46=(24-1)\times2$
$47=2\times24-1$
$48=1\times2\times24$
$49=2\times24+1$
$50=(1+24)\times2$