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    • Green Number 4

      2011 in fours

      5 October, 2011
      2011

      Write the number 2011 using only the digit 4 and any of the operations of addition, subtraction, multiplication, division, exponentiation, taking a square root and factorial. You can use any number composed of the digit 4, even if it's decimal, so 44 and 44.44 are both allowed. You're also allowed to use brackets.

      Have fun!



      This puzzle was contributed by Paulo Ferro, a maths teacher in Oporto, Portugal. For more of Paulo's puzzles, visit his website in English or Portuguese. If you have a puzzle you think might interest Plus readers, please email us!

      Solution link
      2011 in fours - solution
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      Anonymous

      5 October 2011

      Permalink
      Comment

      (44*(44+4))-4444/44

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      Anonymous

      8 May 2012

      In reply to (44*(44+4))-4444/44 by Anonymous

      Permalink
      Comment

      4444/2=2222
      2222-(4x44+44)=2002
      2002+4+4= 2010
      2010+(4/4)=2011

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      Anonymous

      5 October 2011

      Permalink
      Comment

      44*44+(4*4*4)+4+4+4-(4/4)

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      Anonymous

      5 October 2011

      Permalink
      Comment

      4*4*4*4*4*((4/4)+(4/4))-4*4*((4/4)+(4/4))-4-(4/4)=2011.
      4*4*4*4*4*2-4*4*2-4-1=2011.
      2048-32-5=2011.

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      Anonymous

      6 October 2011

      Permalink
      Comment

      Least 4s required maybe.
      (4^4-4)*(4+4)-(4+4/4)

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      Anonymous

      6 October 2011

      Permalink
      Comment

      40320/20 - 5

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      Anonymous

      6 October 2011

      Permalink
      Comment

      2011=44^SQRT(4)+4^(4-4/4)+44/4

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      Anonymous

      22 October 2011

      In reply to From Bassel by Anonymous

      Permalink
      Comment

      2011=44^SQRT(4)+4*4*4+44/4

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      Anonymous

      6 October 2011

      Permalink
      Comment

      ((4^(4 + (4/4)))*(4^1/2)) - 4! - (4*(4^1/2) + (4/4)) - 4

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      Anonymous

      6 October 2011

      Permalink
      Comment

      4444 - ((4*4*4*4*4) + (4*4*4*4*4)) - (4*4*4*4) - ((4*4*4) + (4*4*4)) -4/4

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      Anonymous

      6 October 2011

      Permalink
      Comment

      444*4 + 44*(4 + 4:4) + 4*4 - 4:4 =
      1776 + 220 + 16 - 1 = 2011

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      Anonymous

      6 October 2011

      Permalink
      Comment

      =(4^4)*(4+4)-44+4+4-4/4

      by tanks

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      tkruke

      16 October 2011

      Permalink
      Comment

      This puzzle reminds me of a conjecture made by Donald Knuth. I learned about it from the book "Artificial Intelligence" by Russel & Nordvig, and I quote it from there:

      Knuth conjectured that, starting with the number 4, a sequence of factorial, square root, and floor operations will reach any desired positive integer. For example, we can reach 5 from 4 as follows:

      Floor(Sqr(Sqr(Sqr(Sqr(Sqr((4!)!)))))) = 5

      It would be nice to see if anyone could write 2011 using only one 4 and the mentioned functions!

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      Anonymous

      21 October 2011

      Permalink
      Comment

      ...+4+4+4 + 44/4

      = 2000 + 11

      Is it cheating if I have to use an ellipsis or sigma notation?

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      Marianne

      21 October 2011

      In reply to 4+4+4+4+4+4... by Anonymous

      Permalink
      Comment

      Yes!

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      Anonymous

      2 November 2011

      Permalink
      Comment

      ((((4+4) /.4) * (4/.4)) * (4/.4)) + (44/4) = 2011
      broken down:

      8 / .4 = 20
      4 / .4 = 10

      so (20 * 10) * 10 = 2000

      44/4 = 11

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      Anonymous

      21 November 2011

      Permalink
      Comment

      2011 = (4^4 * 4 * sqrt 4) + (44/4) - 44 -4
      By Krani Lupus

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      Anonymous

      21 November 2011

      Permalink
      Comment

      sqrt 4 * (4^4 * 4 - 4!) + 44/4
      By Krani Lupus

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      Anonymous

      2 December 2011

      Permalink
      Comment

      44^((4+4)/4) + 4!(4-4/4) + 4 - 4/4

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      Anonymous

      13 December 2011

      Permalink
      Comment

      ((4(44/4)-(4/4))*((4((4/44)-(4/4)) + ((44/4)-(4/4)))) + (44/4)

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      Anonymous

      16 December 2011

      Permalink
      Comment

      4^4*4*(spuare root of 4)-44+4+4-4/4
      10 4's

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      Anonymous

      22 December 2011

      Permalink
      Comment

      factorial(4)=24
      4*24*24=2304
      4*(factorial(4))to_the_power(squareroot(4))=2304

      factorial(4)/squareroot(4)=288

      (4+4/4)=5

      2304-288-5=2011

      Solution in eight fours: 4*(factorial(4))to_the_power(squareroot(4))-factorial(4)/squareroot(4)-(4+4/4)

      Barry Daniels

      Ref: plus.maths card in Xmas 2011 New Scientist

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      Anonymous

      22 December 2011

      Permalink
      Comment

      4*4*4*4*4+4*4*4*4*4-44+4+4-(4\4)=
      1024+1024-44+4+4-1=
      2048-44+4+4-1=2011

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      bharathsellvan

      22 January 2012

      Permalink
      Comment

      (4^4)*4+(444+444)+(44+44)+(4+4+4)-(4/4)

      (256)*(4)+(888)+(88)+(12)-1

      1024+888+88+11

      2000+11

      2011

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      Anonymous

      6 April 2012

      Permalink
      Comment

      ((4^4) * 4 * sqrt(4)) - (4!) - (4*4) + 4 - (4/4)

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      Anonymous

      26 April 2012

      Permalink
      Comment

      [500/((4/4)/4)]+(40/4)+(4/4)

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      Anonymous

      31 May 2012

      In reply to [500/((4/4)/4)]+(40/4)+(4/4) by Anonymous

      Permalink
      Comment

      i do belive that 5 and 0 are not the number 4

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      Anonymous

      1 May 2012

      Permalink
      Comment

      How to get to 2011 using all 4's.
      4444 - (444*4) = 2668
      2668 - 444 = 2224
      2224 - (44*4) = 2048
      2048 - 44 = 2004
      2004 + 4 + 4 = 2012
      2012 - 4/4 = 2011

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      Anonymous

      24 May 2012

      Permalink
      Comment

      Solution:
      = 4444/4 + 4444/4 + 44/4 - 444/4 - 4444/4
      = 1111 + 1111 +11 - 111 -111
      = 2233 - 222
      = 2011

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      Anonymous

      30 June 2012

      In reply to Solution: = 4444/4 + 4444/4 + by Anonymous

      Permalink
      Comment

      An excellent answer
      Choi

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      Anonymous

      26 July 2012

      Permalink
      Comment

      I feel there should be a limit on number of times 4 is used. Otherwise, the simplest solution would be to add (4/4) 2011 times ( 4/4+4/4+..................=2011). :-)

      Anil Sharma

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      Anonymous

      3 October 2012

      Permalink
      Comment

      4+4/4(4^4 x4) - 4+4/4(4x4) - 4 - 4/4

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      Anonymous

      16 October 2012

      Permalink
      Comment

      2011 = 4 * 502 + 3
      502 = 125 * 4 + 2
      125 = 31 * 4 + 1
      31 = 4 * 4 * 2 - 1

      1 = 4/4
      2 = sqrt(4)
      3 = 4-4/4
      --> 2011 = (((4 * 4 * sqrt(4) - 4/4) * 4 + 4/4) * 4 + sqrt(4)) * 4 + 4 - 4/4

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      Anonymous

      27 January 2013

      Permalink
      Comment

      2011 = (444+44+4)*4+44-(4/4)
      Also:
      2012 = (444+44+4)*4+44
      2013 = (444+44+4)*4+44+(4/4)

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      Anonymous

      27 April 2013

      Permalink
      Comment

      (4444/4)+(4444+4)-(444/4)-(444/4)+(44/4)

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      Anonymous

      3 May 2013

      Permalink
      Comment

      (256 x 16)/2 - 37 = 2011

      - 256 = 4 to the power of 4
      - 16 = 4 x 4
      - 2 = sqrt 4
      - 37 = 4 x 4 x sqrt4 + 4 + 4/4

      Like I said... I love puzzles with infinite right answers :D

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      Konstantin

      7 November 2016

      Permalink
      Comment

      8000=SQRT(SQRT(SQRT(4!-4)^4!)))
      2011=(8000+44)/4

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