2011 in fours

Submitted by Marianne on October 5, 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!

2011 in fours - solution

Comments

Submitted by Anonymous on October 5, 2011

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

Submitted by Anonymous on May 8, 2012

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

Submitted by Anonymous on October 5, 2011

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

Submitted by Anonymous on October 5, 2011

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.

Submitted by Anonymous on October 6, 2011

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

Submitted by Anonymous on October 6, 2011

40320/20 - 5

Submitted by Anonymous on October 6, 2011

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

Submitted by Anonymous on October 22, 2011

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

Submitted by Anonymous on October 6, 2011

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

Submitted by Anonymous on October 6, 2011

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

Submitted by Anonymous on October 6, 2011

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

Submitted by Anonymous on October 6, 2011

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

by tanks

Submitted by tkruke on October 16, 2011

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!

Submitted by Anonymous on October 21, 2011

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

= 2000 + 11

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

Submitted by Marianne on October 21, 2011

Yes!

Submitted by Anonymous on November 2, 2011

((((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

Submitted by Anonymous on November 21, 2011

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

Submitted by Anonymous on November 21, 2011

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

Submitted by Anonymous on December 2, 2011

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

Submitted by Anonymous on December 13, 2011

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

Submitted by Anonymous on December 16, 2011

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

Submitted by Anonymous on December 22, 2011

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

Submitted by Anonymous on December 22, 2011

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

Submitted by bharathsellvan on January 22, 2012

(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

Submitted by Anonymous on April 6, 2012

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

Submitted by Anonymous on April 26, 2012

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

Submitted by Anonymous on May 31, 2012

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

Submitted by Anonymous on May 1, 2012

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

Submitted by Anonymous on May 24, 2012

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

Submitted by Anonymous on June 30, 2012

An excellent answer
Choi

Submitted by Anonymous on July 26, 2012

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

Submitted by Anonymous on October 3, 2012

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

Submitted by Anonymous on October 16, 2012

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

Submitted by Anonymous on January 27, 2013

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

Submitted by Anonymous on April 27, 2013

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

Submitted by Anonymous on May 3, 2013

(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

Submitted by Konstantin on November 7, 2016

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