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2011 in fours

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2011 in fours

Submitted by Marianne on
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

Permalink Submitted by Anonymous (not verified) on 5 October, 2011
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.

Permalink Submitted by tkruke on 16 October, 2011
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!

Permalink Submitted by Anonymous (not verified) on 21 October, 2011
Comment

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

= 2000 + 11

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

Permalink Submitted by Anonymous (not verified) on 21 November, 2011
Comment

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

Permalink Submitted by Anonymous (not verified) on 13 December, 2011
Comment

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

Permalink Submitted by Anonymous (not verified) on 22 December, 2011
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

Permalink Submitted by bharathsellvan on 22 January, 2012
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

Permalink Submitted by Anonymous (not verified) on 1 May, 2012
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

Permalink Submitted by Anonymous (not verified) on 26 July, 2012
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

Permalink Submitted by Anonymous (not verified) on 27 January, 2013
Comment

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

Permalink Submitted by Anonymous (not verified) on 3 May, 2013
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

Permalink Submitted by Konstantin (not verified) on 7 November, 2016
Comment

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