# Puzzles/Arithmetical puzzles/Four 4s Equal.../Solution

## 1

${\displaystyle {\frac {4+4}{4+4}}}$

## 2

${\displaystyle {\frac {4}{4}}+{\frac {4}{4}}}$

## 3

${\displaystyle {\frac {4+4+4}{4}}}$

## 4

${\displaystyle {\frac {4-4}{4}}+4}$

## 5

${\displaystyle {\frac {4\times 4+4}{4}}}$

## 6

${\displaystyle {\frac {4+4}{4}}+4}$

## 7

${\displaystyle 4+4-{\frac {4}{4}}}$

## 8

${\displaystyle 4+4+4-4\,\!}$

## 9

${\displaystyle 4+4+{\frac {4}{4}}}$

## 10

${\displaystyle 4\times 4-{\frac {4!}{4}}}$

## 11

${\displaystyle 4^{2}-4-{\frac {4}{4}}}$

## 12

${\displaystyle 4+4+{\frac {4^{2}}{4}}}$

## 13

${\displaystyle 4^{2}-4+{\frac {4}{4}}}$

## 14

${\displaystyle 4^{2}-{\frac {4+4}{4}}}$

## 15

${\displaystyle 4\times 4-{\frac {4}{4}}}$

## 16

${\displaystyle 4\times 4+4-4\,\!}$

## 17

${\displaystyle 4\times 4+{\frac {4}{4}}}$

## 18

${\displaystyle 4^{2}+{\frac {4+4}{4}}}$

## 19

${\displaystyle 4^{2}+4-{\frac {4}{4}}}$

## 20

${\displaystyle 4\times \left(4+{\frac {4}{4}}\right)}$

## 21

${\displaystyle 4^{2}+4+{\frac {4}{4}}}$

## 22

${\displaystyle 4!-{\frac {4+4}{4}}}$

## 23

${\displaystyle 4!-{\frac {4^{2}}{4\times 4}}}$

## 24

${\displaystyle 4\times 4+4+4\,\!}$

## 25

${\displaystyle 4!+{\frac {4^{2}}{4\times 4}}}$

## 26

${\displaystyle 4!+{\frac {4+4}{4}}}$

## 27

${\displaystyle 4!+4-{\frac {4}{4}}}$

## 28

${\displaystyle 4!+4+4-4\,\!}$

## 29

${\displaystyle 4!+4+{\frac {4}{4}}}$

## 30

${\displaystyle 4!+{\frac {4\times 4!}{4^{2}}}}$

## 31

${\displaystyle 4^{2}+4^{2}-{\frac {4}{4}}}$

## 32

${\displaystyle 4\times 4+4\times 4\,\!}$

## 33

${\displaystyle 4^{2}+4^{2}+{\frac {4}{4}}}$

## 34

${\displaystyle 4!+4+{\frac {4!}{4}}}$

## 35

${\displaystyle \left({\frac {4!}{4}}\right)^{2}-{\frac {4}{4}}}$

## 36

${\displaystyle \left({\frac {4!}{4}}\right)^{2}+4-4}$

## 37

${\displaystyle \left({\frac {4!}{4}}\right)^{2}+{\frac {4}{4}}}$

## 38

${\displaystyle 4^{2}+4^{2}+{\frac {4!}{4}}}$

## 39

${\displaystyle 4!+4^{2}-{\frac {4}{4}}}$

## 40

${\displaystyle 4!+4^{2}+4-4\,\!}$

## 41

${\displaystyle 4!+4^{2}+{\frac {4}{4}}}$

## 42

${\displaystyle 4!+4!-{\frac {4!}{4}}}$

## 43

${\displaystyle 44-{\frac {4}{4}}}$

• This is the only solution that requires 4410

## 44

${\displaystyle 4!+4!-{\frac {4^{2}}{4}}}$

## 45

${\displaystyle \left({\frac {4!+4}{4}}\right)^{2}-4}$

## 46

${\displaystyle 4!+4^{2}+{\frac {4!}{4}}}$

## 47

${\displaystyle 4!+4!-{\frac {4}{4}}}$

## 48

${\displaystyle 4!+4!+4-4\,\!}$

## 49

${\displaystyle 4!+4!+{\frac {4}{4}}}$

## 50

${\displaystyle {\frac {(4!-4)^{2}}{4+4}}}$