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

Solution to ../

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
$$\frac{4\times4+4}{4}$$

6
$$\frac{4+4}{4}+4$$

7
$$4+4-\frac{4}{4}$$

8
$$4+4+4-4 \,\!$$

9
$$4+4+\frac{4}{4}$$

10
$$4\times4-\frac{4!}{4}$$

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
$$4\times4-\frac{4}{4}$$

16
$$4\times4+4-4 \,\!$$

17
$$4\times4+\frac{4}{4}$$

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
$$4!-\frac{4^2}{4\times4}$$

24
$$4\times4+4+4 \,\!$$

25
$$4!+\frac{4^2}{4\times4}$$

26
$$4!+\frac{4+4}{4}$$

27
$$4!+4-\frac{4}{4}$$

28
$$4!+4+4-4 \,\!$$

29
$$4!+4+\frac{4}{4}$$

30
$$4!+\frac{4\times4!}{4^2}$$

31
$$4^2+4^2-\frac{4}{4}$$

32
$$4\times4+4\times4 \,\!$$

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