2011 in fours - solution
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!
Anonymous
Unless I am missing something but:
444 x 4 - 4 x 4 - 4 - 4/4=1776-16-4-1=1755 ??!!
Marianne
Oops, sorry! We forgot the 4^4. Thanks for spotting that!
Anonymous
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.
Anonymous
I think I have a slightly different solution
4 * 4^4 + 44 * 4! - 4 * 4 * 4 + 4
Though it could stand to be checked.
Anonymous
How about
(44 x 44) + ((4^4) + 44)/4
1936 + (64 + 11)
Anonymous
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
Anonymous
Just 9 of them:
(4! * 4) * (4! - 4) + (4! * 4) - 4 - (4 / 4)
Anonymous
Gather 2011 (4/4)s and add them together.
Anonymous
4+4+4+4+4+4+4+4+4+4+4+4+4+4........+4 - 4/4=2011
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