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.
| 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) | J.K. Choi, Seoul, Korea |
| 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) | J.S.G, Maimonides, 1st Form |
| 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 | J.K. Choi, Seoul, Korea |
| 19 | 4!-4-4/4 | J.K. Choi, Seoul, Korea |
| 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) | Jessi Bramlett, Tulsa, OK J.K. Choi, Seoul, Korea & Trevor Gile, Clovis, CA |
| 26 | 4/4(4!)+sqrt 4 4!+sqrt (4+4-4) | Jessi Bramlett, Tulsa, OK J.K. Choi, Seoul, Korea |
| 27 | 4!+4-4/4 | Jessi Bramlett, Tulsa, OK |
| 28 | (4+4)*4-4 4sqrt 4*4-4 | Edward Levinson, Germantown Academy, PA Kelsey Gile, Fresno, CA |
| 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) | J.K. Choi, Seoul, Korea |
| 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 | Katie Sibel, Germantown Academy, PA |
| 49 | (4!+4!)+4/4 | J.K. Choi, Seoul, Korea |
| 50 | 44+(4!/4) | J.K. Choi, Seoul, Korea |
| 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 | J.K. Choi, Seoul, Korea |
| 57 | (4!-sqrt 4)/.4+sqrt 4 | Mauri Jarvinen, Tampere, Finland |
| 58 | ((4!+4)*sqrt 4)+sqrt 4 | J.K. Choi, Seoul, Korea |
| 59 | (4!-sqrt 4)/.4+4 | Mauri Jarvinen, Tampere, Finland |
| 60 | 4*4*4-4 4^4/4-4 | Carolyn Bedrosian, Germantown Academy, PA Dean Tye, Germantown Academy, PA |
| 61 | (4!+sqrt 4)/.4-4 | Mauri Jarvinen, Tampere, Finland |
| 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 | Kelsey Gile, Fresno, CA |
| 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 | J.K. Choi, Seoul, Korea |
| 73 | (4! C sqrt 4)/4 + 4 using nCr | W.H. Yee, Singapore |
| 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 x 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 | Robin Damion, Nottingham, UK |
| 91 | 4*4!-sqrt 4/.4 | Mauri Jarvinen, Tampere, Finland |
| 92 | 4*4!-sqrt 4-sqrt 4 | Robin Damion, Nottingham, UK |
| 93 | 4*4!-gamm(4)/sqrt 4 (4! C sqrt 4)/4 + 4!(using nCr) | Robin Damion, Nottingham, UK W.H. Yee, Singapore |
| 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 | Robin Damion, Nottingham, UK |
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