Solution to Puzzles/Arithmetical_puzzles/Four_4s_Equal...

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

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