# 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 + 4^{4} - 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!*

## Comments

## There are many ways

4+4+4+4+4+4+4+4+4+4+4+4+4+4........+4 - 4/4=2011

_________503 times_____________________

## A primary school child's answer:

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

## Even fewer 4s

Just 9 of them:

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

## Fewer 4s

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

## How about (44 x 44) + ((4^4)

How about

(44 x 44) + ((4^4) + 44)/4

1936 + (64 + 11)

## Different Solution

I think I have a slightly different solution

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

Though it could stand to be checked.

## It feels more "mathematical"

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.

## Solution is wrong (By Bassel)

Unless I am missing something but:

444 x 4 - 4 x 4 - 4 - 4/4=1776-16-4-1=1755 ??!!

## Oops, sorry! We forgot the

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