Четыре четверки — математическая головоломка по поиску простейшего математического выражения для каждого целого числа от 0 до некоторого максимума, используя лишь общие математические символы и цифры четыре (никакие другие цифры не допускаются). Большинство версий «четырёх четверок» требует, чтобы каждое выражение содержало ровно четыре четверки, но некоторые вариации требуют, чтобы каждое выражение имело минимальное количество четверок.
Сможете сами продолжить дальше 20 эту головоломку ?
Ну кому не охота заморачиваться, под катом еще продолжение до СОТНИ :
| 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 | J.S.G, Maimonides, 1st Form |
| 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 | 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 | 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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