### Ruth Carver's

Challenge: Using four 4's and any operations, try to write equations that have the numbers from 0 to 100 as the answer.

Winning the Spot: The answer for each number and the name of the first person to get it will be posted.

Example: 49 = 4! * (sqrt 4) + (4/4)

In case of a tie, the person who uses the fewest number of operations will win the spot.

Alternate Solutions and their authors will also be posted.

Thanks to my friend and colleague, Paul Seaton, Germantown Academy, for sharing this puzzle with me.

0 44 - 44 Mark Girouard, Miramichi, N.B., Canada
1 (4 + 4 - 4)/4
44/44
Nidhi Kohli, Eastern H.S., NJ
2 (4*4)/(4 + 4)
4/4 + 4/4
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
3 (4 + 4 + 4)/4
(4*4 - 4)/4
4 - 4^(4 - 4)
6th Period Biology, OHHS, Oxon Hill, MD
4 (4 - 4)*4 + 4
[\4/444] (integer of the 4th root of 444)
J.S.G, Maimonides, 1st Form
Daniel Freeman
5 (4*4 + 4)/4
4^(4 - 4) + 4
J.S.G, Maimonides, 1st Form
Michalis Georgiou
6 ((4 + 4)/4) + 4 J.K. Choi, Seoul, Korea
7 (4 + 4) - (4/4)
44/4 - 4
J.K. Choi, Seoul, Korea
8 (4*4) - (4 + 4)
4 + 4 + 4 - 4
J.K. Choi, Seoul, Korea
9 (4/4) + 4 + 4 Michael Krueger, Germantown Academy, PA
10 (44 - 4)/4 J.K. Choi, Seoul, Korea
11 44/(sqrt 4 + sqrt 4)
4/.4 + 4/4
J.S.G, Maimonides, 1st Form
Reefe Brighton, Switzerland
12 (44 + 4)/4 J.K. Choi, Seoul, Korea
13 44/4 + sqrt 4 J.S.G, Maimonides, 1st Form
14 4 + 4 + 4 + sqrt 4
4!/4 + 4 + 4
4! - (4 + 4 + sqrt 4)
4*4(4/sqrt 4)
Robin Damion, Nottingham, UKvJessi Bramlett, Tulsa, OK
J.K. Choi, Seoul, Korea
Trevor Gile, Clovis, CA
15 44/4 + 4 Katie Sibel, Germantown Academy, PA
16 4 + 4 + 4 + 4 Leigh S., Germantown Academy, PA
17 4*4 + 4/4
[\44/44!] (integer of the 44th root of 44!)
Kelsey Gile, Fresno, CA
Daniel Freeman
18 (4! + 4! + 4!)/4
4*4 + 4/√4
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
19 4! - 4 - 4/4
(sqrt4 + 4)/(.4) + 4
J.K. Choi, Seoul, Korea
Clara Damour, Treasure Coast High School, Port St. Lucie, FL
20 (4/4 + 4)*4 Leigh S., Germantown Academy, PA
21 4! - 4 + (4/4) J.K. Choi, Seoul, Korea
22 4*4 + 4 + sqrt 4
4/4(4!) - sqrt 4
4! - ((4 + 4)/4)
44/4*sqrt 4
Robin Damion, Nottingham, UK
Jessi Bramlett, Tulsa, OK
J.K. Choi, Seoul, Korea
Kevin Trotter, Escuela Americana School, El Salvador
23 4! - sqrt 4 + 4/4
4! - 4^(4 - 4)
Jessi Bramlett, Tulsa, OK
J.K. Choi, Seoul, Korea &
Trevor Gile, Clovis, CA
24 4*4 + 4 + 4 Eric Treffeisen, Germantown Academy, PA
25 4! + sqrt 4 - 4/4
4! + 4^(4 - 4)
(4 + 4/4)^√4
Jessi Bramlett, Tulsa, OK
J.K. Choi, Seoul, Korea &
Trevor Gile, Clovis, CA
Reefe Brighton, Switzerland
26 4/4(4!) + sqrt 4
4! + sqrt (4 + 4 - 4)
4 + 44/√4
Jessi Bramlett, Tulsa, OK
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
27 4! + 4 - 4/4 Jessi Bramlett, Tulsa, OK
28 (4 + 4)*4 - 4
4sqrt 4*4 - 4
44 - 4*4
Kelsey Gile, Fresno, CA
Reefe Brighton, Switzerland
29 4! + 4 + 4/4 J.K. Choi, Seoul, Korea &
Trevor Gile, Clovis, CA
30 4! + 4 + 4 - sqrt 4 J.K. Choi, Seoul, Korea
31 ((4 + sqrt 4)! + 4!)/4! Jonas Oberg, Lycksele, Sweden &
32 (4*4) + (4*4) Leigh S., Germantown Academy, PA
33 4! + 4 + sqrt 4/.4 Mauri Jarvinen, Tampere, Finland
34 (4*4*sqrt 4) + sqrt 4
4! + (4!/4) + 4
sqrt(4^4)*sqrt 4 + sqrt 4
J.K. Choi, Seoul, Korea
Trevor Gile, Buchanan H.S., CA
Kevin Trotter, Escuela Americana School, El Salvador
35 4! + 44/4 Norbert Gassel, Seligenstadt, Germany&
Patrick McCaney, Voorhees, NJ
36 (4 + 4)*4 + 4
44 - 4 - 4
37 4! + (4! + sqrt 4)/sqrt 4 Mauri Jarvinen, Tampere, Finland
38 44 - (4!/4) J.K. Choi, Seoul, Korea
39 4! + 4!/(4*.4)
4! + (4 + 4/4)!! [Note: !! is odd factorial]
Mauri Jarvinen, Tampere, Finland
Heiner Marxen, Germany
40 (4! - 4) + (4! - 4)
4*(4 + 4 + √4)
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
41 (4! + sqrt 4)/.4 - 4!
44 - gamma(4)/sqrt 4
Mauri Jarvinen, Tampere, Finland
Robin Damion, Nottingham, UK
42 44 - 4 + sqrt 4
(4! + 4!) - (4!/4)
J.K. Choi, Seoul, Korea
Trevor Gile, Buchanan H.S., CA
43 44 - (4/4) J.K. Choi, Seoul, Korea
44 44 + 4 - 4 Charlene Walls, Miramichi, N.B., Canada
45 44 + 4/4 Robin Damion, Nottingham, UK
46 44 + 4 - sqrt 4
(4! + 4!) - (4/sqrt 4)
J.K. Choi, Seoul, Korea
Trevor Gile, Buchanan H.S., CA
47 (4! + 4!) - 4/4 J.K. Choi, Seoul, Korea
48 (4*4 - 4)*4
4*(4 + 4 + 4)
Reefe Brighton, Switzerland
49 (4! + 4!) + 4/4 J.K. Choi, Seoul, Korea
50 44 + (4!/4)
44 + 4 + √4
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
51 (4! - 4 + .4)/.4
4! + 4! + gamma(4)/sqrt 4
Mauri Jarvinen, Tampere, Finland
Robin Damion, Nottingham, UK
52 (44 + 4) + 4 Meghan Flieger, Miramichi, N.B., Canada
53 4! + 4! + sqrt 4/.4 Mauri Jarvinen, Tampere, Finland
54 4! + 4! + 4 + sqrt 4 J.K. Choi, Seoul, Korea
55 (4! - 4 + sqrt 4)/.4 Mauri Jarvinen, Tampere, Finland
56 4! + 4! + 4 + 4
4*(4*4 - √4)
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
57 (4! - sqrt 4)/.4 + sqrt 4 Mauri Jarvinen, Tampere, Finland
58 ((4! + 4)*sqrt 4) + sqrt 4
4! + 4! + 4/.4
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
59 (4! - sqrt 4)/.4 + 4
4!/.4 - 4/4
Mauri Jarvinen, Tampere, Finland
Reefe Brighton, Switzerland
60 4*4*4 - 4
4^4/4 - 4
44 + 4*4
Reefe Brighton, Switzerland
61 (4! + sqrt 4)/.4 - 4
4!/.4 + 4/4
Mauri Jarvinen, Tampere, Finland
Reefe Brighton, Switzerland
62 4*4*4 - sqrt 4 Robin Damion, Nottingham, UK
63 (4^4 - 4)/4 Sung-II Kim, Yonsei University, Seoul, Korea &
64 4sqrt 4*4sqrt 4
4*(4! - 4 - 4)
(4 + 4)*(4 + 4)
Kelsey Gile, Fresno, CA
Reefe Brighton, Switzerland
Reefe Brighton, Switzerland
65 (4^4 + 4)/4 L.C., Orlando, FL
66 4*4*4 + sqrt 4 Robin Damion, Nottingham, UK
67 (4! + sqrt 4)/.4 + sqrt 4 Mauri Jarvinen, Tampere, Finland
68 4*4*4 + 4
4^4/4 + 4
69 (4! + sqrt 4)/.4 + 4 Mauri Jarvinen, Tampere, Finland
70 (4 + 4)!/(4!*4!)
44 + 4! + sqrt 4
Robin Damion, Nottingham, UK
J.K. Choi, Seoul, Korea
71 (4! + 4.4)/.4 Mauri Jarvinen, Tampere, Finland
72 44 + 4! + 4
4*(4*4 + √4)
J.K. Choi, Seoul, Korea
Reefe Brighton, Switzerland
73 (4! C sqrt 4)/4 + 4 using nCr
(.4√4 + .4)/.4...** (see below)
W.H. Yee, Singapore
Reefe Brighton, Switzerland
74 4! + 4! + 4! + sqrt 4 J.K. Choi, Seoul, Korea
75 (4! + 4 + sqrt 4)/.4 Mauri Jarvinen, Tampere, Finland
76 (4! + 4! + 4!) + 4 J.K. Choi, Seoul, Korea
77 ((4 - gamma(sqrt4))^4 ) - 4
(4/.4repeating)^sqrt4 - 4
Tan Chee How, Ngee Ann Polytechnic, Singapore
W.H. Yee, Singapore
78 4*(4! - 4) - sqrt 4 Mauri Jarvinen, Tampere, Finland
79 4! + (4! - sqrt 4)/.4 Mauri Jarvinen, Tampere, Finland
80 (4*4 + 4)*4 Leigh S., Germantown Academy, PA
81 (4 - (4/4))^4
(4!/(4*sqrt 4))^4
(4 - (log4/log4))^4
Trevor Gile, Buchanan H.S., CA
Robin Damion, Nottingham, UK
J.K. Choi, Seoul, Korea
82 4*(4! - 4) + sqrt 4 Mauri Jarvinen, Tampere, Finland
83 (4! - .4)/.4 + 4! Mauri Jarvinen, Tampere, Finland
84 44*sqrt 4 - 4 Trevor Gile, Buchanan H.S., CA
85 (4! + 4/.4)/.4 Mauri Jarvinen, Tampere, Finland
86 44*sqrt 4 - sqrt 4 Robin Damion, Nottingham, UK
87 4*4! - 4 / 0.bar4
44*sqrt(4) -i^4
((4 - gamma(sqrt4))^4) + (gamma 4)
Carrie Lineberry, North Carolina
Chua Soo Nam, Lecturer, Ngee Ann Polytechnic, Singapore
88 4*4! - 4 - 4
44 + 44
Robin Damion, Nottingham, UK
89 4! + (4! + sqrt 4)/.4 Mauri Jarvinen, Tampere, Finland
90 4*4! - 4 - sqrt 4
44*√4 + √4
Robin Damion, Nottingham, UK
Reefe Brighton, Switzerland
91 4*4! - sqrt 4/.4 Mauri Jarvinen, Tampere, Finland
92 4*4! - sqrt 4 - sqrt 4
44*√4 + 4
Robin Damion, Nottingham, UK
Reefe Brighton, Switzerland
93 4*4! - gamm(4)/sqrt 4
(4! C sqrt 4)/4 + 4!(using nCr)
4 * 4! - (4/.4)
Robin Damion, Nottingham, UK
W.H. Yee, Singapore
Reefe Brighton, Switzerland
94 4*4! + sqrt 4 - 4 Robin Damion, Nottingham, UK
95 4*4! - 4/4 Robin Damion, Nottingham, UK
96 4*4! + 4 - 4
4! + 4! + 4! + 4!
Robin Damion, Nottingham, UK
J.K. Choi, Seoul, Korea
97 4*4! + 4/4 Robin Damion, Nottingham, UK
98 4*4! + 4 - sqrt 4 Robin Damion, Nottingham, UK
99 44/.44(repeating)
4*4! + gamma(4)/sqrt 4
4/4% - 4/4
(4 * 4!) + sqrt (4)/sqrt(.0 bar 4)
Neil Vasan, Vienna, WV
Robin Damion, Nottingham, UK
W.H. Yee, Singapore
Nina Teicholz, San Francisco
100 4*4! + sqrt 4 + sqrt 4
4/.4*4/.4
44/.44
Robin Damion, Nottingham, UK
Reefe Brighton, Switzerland
Reefe Brighton, Switzerland

** Denotes the sum of the .4th root of 4 plus .4, all divided by 0.4 repeating.