<pre>
<pre>
 1  <code> (4+4-4)/4 </code> 44/44

 2  <code> (4*4)/(4+4) </code> (4+4+4)/4

 3  <code> (4*4-4)/4 </code> 4-4^(4-4)

 4  = (4-4)*4+4

 5  = (4*4+4)/4

 6  = ((4+4)/4)+4

 7  <code> (4+4)-(4/4) </code> 44/4-4

 8  <code> (4*4)-(4+4) </code> 4+4+4-4

 9  = (4/4)+4+4

10  = (44-4)/4

11  = 44/(sqrt 4+sqrt 4)

12  = (44+4)/4

13  <code> 44/4+sqrt 4 </code> 4+4+4+sqrt 4

14  <code> 4====/4+4+4 </code> 4!-(4+4+sqrt 4) = 4*4(4/sqrt 4)
====

15  = 44/4+4

16  = 4+4+4+4

17  = 4*4+4/4

18  = (4====+4!+4!)/4
====

19  = 4====-4-4/4
====

20  = (4/4+4)*4

21  <code> 4====-4+(4/4) </code> 4*4+4+sqrt 4
====

22  <code> 4/4(4====)-sqrt 4 </code> 4!-((4+4)/4) = 44/4*sqrt 4
====

23  <code> 4====-sqrt 4+4/4 </code> 4!-4^(4-4)
====

24  = 4*4+4+4

25  <code> 4====+sqrt 4-4/4 </code> 4!+4^(4-4)
====

26  <code> 4/4(4====)+sqrt 4 </code> 4!+sqrt (4+4-4)
====

27  = 4====+4-4/4
====

28  <code> (4+4)'''4-4 </code> 4sqrt 4'''4-4

29  = 4====+4+4/4
====

30  = 4====+4+4-sqrt 4
====

31  = ((4+sqrt 4)====+4!)/4!
====

32  = (4'''4)+(4'''4)

33  <code> 4====+4+sqrt 4/.4 </code> (4'''4'''sqrt 4)+sqrt 4
====

34  <code> 4====+(4!/4)+4 </code> sqrt(4^4)*sqrt 4+sqrt 4
====

35  = 4====+44/4
====

36  <code> (4+4)*4+4 </code> 44-4-4

37  = 4====+(4!+sqrt 4)/sqrt 4
====

38  = 44-(4====/4)
====

39  = 4====+4!/(4*.4)
====

40  = (4====-4)+(4!-4)
====

41  = (4====+sqrt 4)/.4-4!
====

42  <code> 44-4+sqrt 4 </code> (4====+4!)-(4!/4)
====

43  = 44-(4/4)

44  = 44+4-4

45  = 44+4/4

46  <code> 44+4-sqrt 4 </code> (4====+4!)-(4/sqrt 4)
====

47  = (4====+4!)-4/4
====

48  = (4'''4-4)'''4

49  = (4====+4!)+4/4
====

50  = 44+(4====/4)
====

51  = (4====-4+.4)/.4
====

52  = (44+4)+4

53  = 4====+4!+sqrt 4/.4
====

54  = 4====+4!+4+sqrt 4
====

55  = (4====-4+sqrt 4)/.4
====

56  = 4====+4!+4+4
====

57  = (4====-sqrt 4)/.4+sqrt 4
====

58  = ((4====+4)*sqrt 4)+sqrt 4
====

59  = (4====-sqrt 4)/.4+4
====

60  <code> 4'''4'''4-4 </code> 4^4/4-4

61  = (4====+sqrt 4)/.4-4
====

62  = 4'''4'''4-sqrt 4

63  = (4^4-4)/4

64  = 4sqrt 4*4sqrt 4

65  = (4^4+4)/4

66  = 4'''4'''4+sqrt 4

67  = (4====+sqrt 4)/.4+ sqrt 4
====

68  <code> 4'''4'''4+4 </code> 4^4/4+4

69  = (4====+sqrt 4)/.4+4
====

70  <code> (4+4)====/(4!*4!) </code> 44+4!+sqrt 4
====

71  = (4====+4.4)/.4
====

72  = 44+4====+4
====

73

74  = 4====+4!+4!+sqrt 4
====

75  = (4====+4+sqrt 4)/.4
====

76  = (4====+4!+4!)+4
====

77

78  = 4*(4====-4)-sqrt 4
====

79  = 4====+(4!-sqrt 4)/.4
====

80  <code> (4'''4+4)'''4 </code> (4-(4/4))^4

81  = (4====/(4*sqrt 4))^4
====

82  = 4*(4====-4)+sqrt 4
====

83  = (4====-.4)/.4+4!
====

84  = 44*sqrt 4-4

85  = (4====+4/.4)/.4
====

86  = 44*sqrt 4-sqrt 4

87

88  <code> 4*4====-4-4 </code> 44+44
====

89  = 4====+(4!+sqrt 4)/.4
====

90  = 4*4====-4-sqrt 4
====

91  = 4*4====-sqrt 4/.4
====

92  = 4*4====-sqrt 4-sqrt 4
====

93

94  = 4*4====+sqrt 4-4
====

95  = 4*4====-4/4
====

96  <code> 4*4====+4-4 </code> 4!+4!+4!+4!
====

97  = 4*4====+4/4
====

98  = 4*4====+4-sqrt 4
====

99

100 = 4*4====+sqrt 4+sqrt 4
====

101 = 4*4====+sqrt 4/.4
====

102 = 4*4====+4+sqrt 4
====

103

104 = 4*4====+4+4
====

105 = (44-sqrt 4)/.4

106 = 4*4====+4/.4
====

107

108 = 4*(4====+4)-4
====

109 = (44-.4)/.4

110 = (4====+4!-.4)/.4
====

111 = 444/4

112 = (44/.4)+sqrt 4
</pre>

References

M Bicknell and V E Hoggatt, ''Recreational Mathematics Magazine'',
No 14 (1964).  Shows 64 ways to make 64 with four fours.  Good
list of references.

L Harwood Clarke, ''Fun With Figures'', William Heinemann Ltd, 1954,
pp 51-53.  Contains a table for the four fours problem from 1 to
100.

Henry Ernest Dudeney, ''536 Puzzles and Curious Problems'',
Charles Scribner's Sons, 1967.  SBN 684-71755-7, Library of Congress
Card Number 67-15488.  Puzzle 109.  Cites ''Knowledge'' article below.

Angela Dunn, ''Mathematical Bafflers'', McGraw-Hill, 1964, pp 51-53.
Also contains a table for the four fours problem from 1 to 100.

Martin Gardner, "Mathematical Games."  In ''Scientific American'',
January 1964.  Contains a more recent discussion of the problem.
The following month's issue contains the solutions to posed
questions.

Don Knuth, "Representing Numbers Using Only One 4."  In
''Mathematics Magazine'', Vol 37, November/December 1964, pp. 308-10.
Shows how numbers up to 208 may be represented using only one
four, square roots, factorials and brackets [[floor]].  Conjectures
that all integers can be represented in this way.

''Knowledge'', ed Richard Proctor, 30 December 1881.  A magazine of
popular science edited by astronomer Proctor.
</pre>
