### Four 4's Part 2

Using arithmetic combinations of four 4's express the integers from 11 to 20.

You must use all four 4's for each number.

You may combine the 4's using the arithmetic operations +, -, * (multiplication) and / (division).

You are also allowed to use sqrt (square root) (e.g. sqrt(4) ). Y

ou are allowed to use concatenation (e.g. 44 is valid as part of an answer).

You are allowed to use factorials. For example, 4! (or factorial(4)) = 4*3*2*1 = 24. (The factorial of an integer x! is the product of all the positive integers less than or equal to x).

You do not need to use anything more exotic than those listed above - so no decimal places, powers of 4, trig operations, logarithms, cube/quartic/etc. roots, etc.

## 1 Comments:

11 = 4!/sqrt(4) - 4/4

12 = 4!/sqrt(4) * 4/4

13 = 4!/sqrt(4) + 4/4

14 = 4+4+4 + sqrt(4)

15 = 4*4 - 4/4

16 = 4+4+4+4

17 = 4*4 + 4/4

18 = 4*4 + 4/sqrt(4)

19 = 4! - 4 - 4/4

20 = (4! - 4) * (4/4)

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