Challenge: Using the digits in 1996 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: For 1995, some possible equations were
0 = 1*(9-9)*5
2 = (19-9)/5
etc.The numbers need not be in order but in case of a tie, the person who got the answer without rearranging the digits or by using the least number of operations will win the spot.
Alternate Solutions and their authors will also be posted for answers with the digits in order and the least number of operations used.
Thanks to my friend and colleague, Dick Davies of Germantown Academy, for sharing this activity with me.
Submit An Answer:: If you think you have an equation that equals any of the numbers not yet answered, Send It In!
| Answer | Equation | Submitted by |
|---|---|---|
| 0 | (9-9)/16 (1*9-9)*6 | Niko Alejandre Brent Tworetzky |
| 1 | (9-9)*6+1 1+(9-9)^6 1^996 199mod6 | Matt Breen Chrissy Seelaus Karthik Bala Mike Creveling |
| 2 | 1+(sqrt 9+sqrt 9)/6 1/9*sqrt 9*6 | Niko Alejandre Mitchell Beer |
| 3 | 1(9+9)/6 6/((9/9)+1) | Chris Krug Louis Rubinfield |
| 4 | 1^9+9-6 1+(9+9)/6 19-9-6 | Deborah Zickler Chris Krug Robin Damion |
| 5 | (9/9)*6-1 -1(9/9)+6 | Chris Krug Richard Tapnio |
| 6 | 1(9-9)+6 1^99*6 | Rich Weber Craig Cramer Dean Tye & Mike K. |
| 7 | 1+9-9+6 (1*9)/9+6 1^9^9+6 | Jon Goldberg Lauren Kupersmith Dean Tye & Mike K. |
| 8 | 1+9/9+6 | Valeria Kukla |
| 9 | 1^96*9 1*9/sqrt 9+6 | Danielle Ruppel Jeffrey Chang |
| 10 | 19-sqrt 9-6 | Mitchell Beer |
| 11 | 9+9-6-1 1/sqrt 9*6+9 -1+9+9-6 | Michael Krueger & Mike Lavner Oak Hill Academy Richard Tapnio |
| 12 | 1(9+9-6) 1*9+9-6 | Fish & Doog TJ Jackson |
| 13 | 1+9+9-6 sqrt 1 +sqrt 9+sqrt 9+6 | Chris Goodchild Richard Tapnio |
| 14 | 9+6-1^9 -1+(sqrt (9*9))+6 (-1)^9+9+6 | Jeffrey Chang Paul Seaton Erik DiGuilio |
| 15 | ((1+9)*9)/6 | Mitchell Beer |
| 16 | 1^9 +9+6 19-9+6 | Harris Dainoff Robin Damion |
| 17 | 6*9/sqrt 9-1 -1+(sqrt 9)!+(sqrt 9)! +6 | Jeffrey Chang Kevin Lai |
| 18 | (9-6-1)9 1*9+sqrt 9+6 | Fish & Doog Mitchell Beer |
| 19 | 1+9/sqrt 9*6 1+(sqrt 9)!+(sqrt 9)!+6 9) | Jeffrey Chang Kevin Lai |
| 20 | (1+9)/sqrt 9*6 | Jeffrey Chang |
| 21 | 19+6/sqrt 9 1*sqrt (9*9)-6 | Jeffrey Chang Shikha Bhan |
| 22 | 19-sqrt 9+6 19+9-6 | Mitchell Beer Robin Damion |
| 23 | 9+9+6-1 -1+9+9+6 | Edward Levinson Jared Schwennesen |
| 24 | (9-1)*(9-6) 1(9+9)+6 (1-9)(-9+6) & 1*9+9+6 | Deborah Zickler Lauren Hillman Brent Tworetzky |
| 25 | 1+9+9+6 | Matt Breen |
| 26 | (9-6)9-1 (-1)^9+sqrt(sqrt(9^6)) | Fish & Doog Erik DiGuilio |
| 27 | 1*9(9-6) | Fish & Doog |
| 28 | (9-6)9+1 19+sqrt 9+6 | Fish & Doog Mitchell Beer |
| 29 | -1-sqrt(9)!+(sqrt(9)!)*6 sqrt(1+(sqrt(9)!!)/(sqrt(9)!)+6!) -1+sqrt(9)+sqrt((sqrt(9)^6)) | Sergey Markelov |
| 30 | (1+9)(9-6) | Matt Breen, Adam Hilton |
| 31 | 96/sqrt 9-1 1+sqrt 9+sqrt(sqrt(9^6)) | Oak Hill Academy Erik DiGuilio |
| 32 | 96/sqrt 9*1 -1+sqrt 9*9+6 | Oak Hill Academy Denis Denisenko |
| 33 | 96/sqrt 9+1 1*sqrt 9 *9+6 | Oak Hill Academy Zach Grabowski |
| 34 | 19+9+6 | Lauren Kupersmith |
| 35 | 9*6-19 -1+9+sqrt(sqrt(9^6)) | Oak Hill Academy Erik DiGuilio |
| 36 | (1-6+9)9 (1+sqrt 9)(sqrt 9 +6) | Fish & Doog Brent Tworetzsky |
| 37 | 1+(sqrt 9)((sqrt 9)!+6) | Brent Tworetzsky |
| 38 | 99-61 (19/sqrt 9)*6 | Dean Tye Nidhi Kohli & Samantha Levy |
| 39 | (9-1)*6-9 (1+(sqrt9))!+9+6 | Oak Hill Academy Denis Denisenko |
| 40 | (6-1)!*sqrt 9/9 1+sqrt 9+(sqrt9)!*6 | Robin Damion Denis Denisenko |
| 41 | -1+sqrt(9)!+(sqrt(9)!)*6 | Sergey Markelov |
| 42 | (6+1)*(sqrt 9+sqrt 9) (1+sqrt 9+sqrt 9)*6 | Roger Day Gayle Chan |
| 43 | 61-9-9 1+(sqrt9)!+(sqrt9)!*6 | Richard Tapnio Denis Denisenko |
| 44 | 6*9-9-1 -1-9+(9*6) | Fish & Doog Todd Nocella |
| 45 | 6*9-9*1 1*sqrt 9(9+6) | Fish & Doog Denis Denisenko |
| 46 | 6*9-9+1 1+sqrt 9(9+6) | Fish & Doog Denis Denisenko |
| 47 | 9*6-(sqrt 9)!-1 -1+9(sqrt9)!-6 | Roger Day Denis Denisenko |
| 48 | (1+sqrt 9)((sqrt 9)!+6) | Brent Tworetzsky |
| 49 | 61-9- sqrt 9 1+9(sqrt9)!-6 | Roger Day, Oak Hill Academy Denis Denisenko |
| 50 | 69-19 (1+9)sqrt 9/.6 | Harris Dainoff Denis Denisenko |
| 51 | ((9*6)-sqrt 9)/1 -(1*sqrt 9-9*6) 19*sqrt 9-6 | Roger Day Jennifer Buxton David Hoel |
| 52 | 1+9*6-sqrt 9 -(-1+sqrt 9-9*6) | Kate Sibel Jennifer Buxton |
| 53 | -1+sqrt 9*sqrt 9*6 -1^9+9*6 | Brent Tworetzsky The Learning Kingdom |
| 54 | (1+6)*9-9 1*sqrt 9*sqrt 9*6 | Mike Krueger Brent Tworetzky |
| 55 | 9*6+1^9 1^9+9*6 1+(sqrt 9*sqrt 9*6) | Richard Tapnio Dean Tye & Mike K. Brent Tworetzsky |
| 56 | 9!/6!/9*1 (1*9!/9)/6! | Adam Hilton Brent Tworetzsky |
| 57 | 19(9-6) | Lauren Kupersmith |
| 58 | 9*6+sqrt 9+1 1+sqrt 9+9*6 | Roger Day Zach Riggin |
| 59 | 69-9-1 -1+9(sqrt9)!+6 | Richard Tapnio Denis Denisenko |
| 60 | (19-9)*6 | Lauren Kupersmith |
| 61 | 69-(9-1) 1+9(sqrt9)!+6 | Richard Tapnio Denis Denisenko |
| 62 | 9*6+9-1 -1+9+9*6 | Eric Treffeisen, Brian Coombs Codi Williams |
| 63 | 1*9+9*6 | Jessie Anders |
| 64 | 1+9+9*6 | Fish & Doog |
| 65 | 9*9-16 | The Learning Kingdom |
| 66 | (9-1)*9-6 (-1+9)*9-6 | Michael Stamm Dean Tye & Mike K. |
| 67 | 61-sqrt 9+9 | Mike & Ray Williams, Oak Hill Academy |
| 68 | 69-1^9 | The Learning Kingdom |
| 69 | (1+9)6+9 | Fish & Doog |
| 70 | 69+1^9 (1+sqrt 9)^sqrt 9+6 | Deborah Zickler Denis Denisenko |
| 71 | (9+sqrt
9)*6-1 (6!/9)-(1*9) sqrt(1+(9/9+6)!) | Nick
Canizares Craig Trachtenburg Denis Denisenko |
| 72 | 9*(6+1)+9 (1+sqrt 9)(sqrt 9*6) (9-1^6)*9 | Dean Tye & Mike K. Brent Tworetzsky Mike Krueger |
| 73 | 19+(9*6) | Lauren Kupersmith |
| 74 | 9*9-6-1 -1+(9*9)-6 | Jennifer
Kleiner, Mark Wakeman, & Jacquelyn Kunkel Dean Tye & Mike K. |
| 75 | 1*9*9-6 | Ben Haaz |
| 76 | 1+(9*9)-6 | Deborah Zickler |
| 77 | 96-19 -19+96 | Katie Gupton Erik DiGuillio & Robert Joyner |
| 78 | 69+9*1 (-1+9)*9+6 | Richard Tapnio Dean Tye & Mike K. |
| 79 | 61+9+9 | Deborah Zickler |
| 80 | 9*9-1^6 -1+sqrt 9*sqrt(sqrt(9^6)) | Brian Coombs Erik DiGulio |
| 81 | (9*9)*1^6 1(9(sqrt 9 +6)) | Michael Beautyman Greg Mellor |
| 82 | 1^6+(9x9) 1+sqrt 9*sqrt(sqrt(9^6)) | Katie Sibel Erik DiGulio |
| 83 | 99-16 -1+9!/(sqrt9)!!/6 | Adam Hilton Denis Denisenko |
| 84 | (1+9)*9-6 | Marian Ramirez |
| 85 | 9*9+sqrt 16 1+9!/(sqrt9)!!/6 | Josh Boehm Denis Denisenko |
| 86 | -1+9*9+6 | Tracey Elliott |
| 87 | 1*9*9+6 | Carolyn Bedrosian |
| 88 | 1+9*9+6 | Rich Weber |
| 89 | 1*9+(6!/9) | Richard Tapnio |
| 90 | 1+9+(6!/9) | Richard Tapnio |
| 91 | 91/Int(9/6) sqrt(91^(6/sqrt 9)) 1-(sqrt9)!+96 | Ron Gutmark Todd Nocella Denis Denisenko |
| 92 | 99-6-1 -1+99-6 | Leigh S. Adam Hilton |
| 93 | 1*99-6 | Lauren Kupersmith |
| 94 | 1+99-6 | Chris Cunningham |
| 95 | -1^9+96 | Mike Creveling |
| 96 | 9(1+9)+6 (1+9)*9+6 | Brandon Fishman Dean Tye |
| 97 | 9*9+16 1^9+96 | Matt Breen The Learning Kingdom |
| 98 | 99-1^6 -1+sqrt 9+96 | Deborah Zickler Denis Denisenko |
| 99 | 99/1^6 1*sqrt 9+96 | Deborah Zickler Denis Denisenko |
| 100 | 1^6+99 1+sqrt 9+96 | Deborah Zickler Dan Smith |
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