Τετάρτη, 4 Οκτωβρίου 2017

Μαθηματική πρόκληση: Τέσσερα τεσσάρια

Χρησιμοποιώντας τέσσερα τεσσάρια και οποιαδήποτε από τις τέσσερις πράξεις και δυνάμεις, ριζικά, παραγοντικά να σχηματίσετε τους αριθμούς από το $0$ έως $100$.
Answer          Equation                   Submitted by         
0 44 - 44 Mark Girouard, Miramichi, N.B., Canada
1 (4 + 4 - 4)/4
 44/44
 Leigh S., Germantown Academy, PA
 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)
 Ryan McDonald, Miramichi, N.B., Canada
 Nicole Finelli, Germantown Academy, PA
 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
 Nathan O'Reilley, Miramichi, N.B., Canada
8 (4*4) - (4 + 4)
 4 + 4 + 4 - 4
 J.K. Choi, Seoul, Korea
 Daniel Moffitt, Miramichi, N.B., Canada
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
 (4*4 + 4) - √4
 J.K. Choi, Seoul, Korea
 Reefe Brighton, Switzerland
 Noah B., Downers Grove, IL
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
 Edward Levinson, Germantown Academy, PA
 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 &
 Norbert Gassel, Seligenstadt, Germany
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
 Dean Tye, Germantown Academy, PA
 Carolyn Bedrosian, Germantown Academy, PA
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)
 Katie Sibel, Germantown Academy, PA
 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
 Carolyn Bedrosian, Germantown Academy, PA
 Dean Tye, Germantown Academy, PA
 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 &
 Chris Bagan, Edmonton, Alberta, Canada
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
 Laura Whitty, Miramichi, N.B., Canada
 Katie Sibel, Germantown Academy, PA
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)
 Denis Silcock, MILTON, Ontario, Canada
 Carrie Lineberry, North Carolina
 Chua Soo Nam, Lecturer, Ngee Ann Polytechnic, Singapore
88 4*4! - 4 - 4
 44 + 44
 Robin Damion, Nottingham, UK
 Darren Richardson, Miramichi, N.B., Canada
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.
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