View source for Puzzles/Arithmetical puzzles/Four 4s Equal.../Solution

{{Wikipedia|Four fours}}
Solution to [[../]]

==1==
<math>\frac{4+4}{4+4}</math>

==2==
<math>\frac{4}{4}+\frac{4}{4}</math>

==3==
<math>\frac{4+4+4}{4}</math>

==4==
<math>\frac{4-4}{4}+4</math>

==5==
<math>\frac{4\times4+4}{4}</math>

==6==
<math>\frac{4+4}{4}+4</math>

==7==
<math>4+4-\frac{4}{4}</math>

==8==
<math>4+4+4-4 \,\!</math>

==9==
<math>4+4+\frac{4}{4}</math>

==10==
<math>4\times4-\frac{4!}{4}</math>

==11==
<math>4^2-4-\frac{4}{4}</math>

==12==
<math>4+4+\frac{4^2}{4}</math>

==13==
<math>4^2-4+\frac{4}{4}</math>

==14==
<math>4^2-\frac{4+4}{4}</math>

==15==
<math>4\times4-\frac{4}{4}</math>

==16==
<math>4\times4+4-4 \,\!</math>

==17==
<math>4\times4+\frac{4}{4}</math>

==18==
<math>4^2+\frac{4+4}{4}</math>

==19==
<math>4^2+4-\frac{4}{4}</math>

==20==
<math>4\times\left(4+\frac{4}{4}\right)</math>

==21==
<math>4^2+4+\frac{4}{4}</math>

==22==
<math>4!-\frac{4+4}{4}</math>

==23==
<math>4!-\frac{4^2}{4\times4}</math>

==24==
<math>4\times4+4+4 \,\!</math>

==25==
<math>4!+\frac{4^2}{4\times4}</math>

==26==
<math>4!+\frac{4+4}{4}</math>

==27==
<math>4!+4-\frac{4}{4}</math>

==28==
<math>4!+4+4-4 \,\!</math>

==29==
<math>4!+4+\frac{4}{4}</math>

==30==
<math>4!+\frac{4\times4!}{4^2}</math>

==31==
<math>4^2+4^2-\frac{4}{4}</math>

==32==
<math>4\times4+4\times4 \,\!</math>

==33==
<math>4^2+4^2+\frac{4}{4}</math>

==34==
<math>4!+4+\frac{4!}{4}</math>

==35==
<math>\left(\frac{4!}{4}\right)^2-\frac{4}{4}</math>

==36==
<math>\left(\frac{4!}{4}\right)^2+4-4</math>

==37==
<math>\left(\frac{4!}{4}\right)^2+\frac{4}{4}</math>

==38==
<math>4^2+4^2+\frac{4!}{4}</math>

==39==
<math>4!+4^2-\frac{4}{4}</math>

==40==
<math>4!+4^2+4-4 \,\!</math>

==41==
<math>4!+4^2+\frac{4}{4}</math>

==42==
<math>4!+4!-\frac{4!}{4}</math>

==43==
<math>44-\frac{4}{4}</math>
*<small>This is the only solution that requires 44<sub>10</sub></small>

==44==
<math>4!+4!-\frac{4^2}{4}</math>

==45==
<math>\left(\frac{4!+4}{4}\right)^2-4</math>

==46==
<math>4!+4^2+\frac{4!}{4}</math>

==47==
<math>4!+4!-\frac{4}{4}</math>

==48==
<math>4!+4!+4-4 \,\!</math>

==49==
<math>4!+4!+\frac{4}{4}</math>

==50==
<math>\frac{(4!-4)^2}{4+4}</math>

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