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

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

1

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

2

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

3

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

4

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

5

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

6

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

7

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

8

$4+4+4-4\,\!$

9

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

10

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

11

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

12

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

13

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

14

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

15

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

16

$4\times 4+4-4\,\!$

17

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

18

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

19

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

20

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

21

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

22

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

23

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

24

$4\times 4+4+4\,\!$

25

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

26

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

27

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

28

$4!+4+4-4\,\!$

29

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

30

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

31

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

32

$4\times 4+4\times 4\,\!$

33

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

34

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

35

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

36

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

37

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

38

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

39

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

40

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

41

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

42

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

43

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

• This is the only solution that requires 44₁₀

44

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

45

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

46

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

47

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

48

$4!+4!+4-4\,\!$

49

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

50

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