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    • 2011 in fours - solution

      1 November, 2011
      2011

      Write the number 2011 using only the digit 4 and 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.

      Solution: 444 x 4 + 44 - 4 x 4 - 4 - 4/4 = 2011.


      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!

      Back to original puzzle

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      Anonymous

      1 November 2011

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      Comment

      Unless I am missing something but:
      444 x 4 - 4 x 4 - 4 - 4/4=1776-16-4-1=1755 ??!!

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      Marianne

      2 November 2011

      In reply to Solution is wrong (By Bassel) by Anonymous

      Permalink
      Comment

      Oops, sorry! We forgot the 4^4. Thanks for spotting that!

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      Anonymous

      29 November 2011

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      Comment

      It feels more "mathematical" to me to just do 4/4 + 4/4 + 4/4 + ... and keep going for 2011 terms. More "mathematical" because it's trivial to generalise to any natural number, and from there it's trivial to generalise to any integer, rational or surd.

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      Anonymous

      2 December 2011

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      Comment

      I think I have a slightly different solution

      4 * 4^4 + 44 * 4! - 4 * 4 * 4 + 4

      Though it could stand to be checked.

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      Anonymous

      10 May 2012

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      Comment

      How about

      (44 x 44) + ((4^4) + 44)/4
      1936 + (64 + 11)

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      Anonymous

      3 June 2012

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      Comment

      I've managed to get a solution using 10 4s, as opposed to 11, might be fun to see the equation which uses the fewest number of 4s.
      Here's mine:
      44^(sqrt(4))+(4*4!)-(4*4)-4-(4/4)
      Which gives
      44^2+(4*24)-16-4-1
      =
      1936+96-16-4-1 =2011

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      Anonymous

      9 July 2012

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      Comment

      Just 9 of them:
      (4! * 4) * (4! - 4) + (4! * 4) - 4 - (4 / 4)

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      Anonymous

      9 September 2012

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      Comment

      Gather 2011 (4/4)s and add them together.

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      Anonymous

      29 September 2014

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      Comment

      4+4+4+4+4+4+4+4+4+4+4+4+4+4........+4 - 4/4=2011
      _________503 times_____________________

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