### Four 4's

Using arithmetic combinations of four 4's express the numbers from 1 to 10.

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)=2, sqrt(4/4)=1).

You do not need to use concatenation (e.g. 44), decimal places (e.g. 4.4), factorials (e.g. 4!), or trig functions such as sin or cos.

## 3 Comments:

Some parentheses omitted!

1=4/4 * 4/4

2=4/4 + 4/4

3=4/4 + 4/sqrt(4)

4=(4*4)/(sqrt(4)*sqrt(4))

5=(4*sqrt(4)+sqrt(4)) / sqrt(4)

6=(4+4+4)/sqrt(4)

7=4+4-4/4

8=4+4+4-4

9=4+4+4/4

10=4+4+4-sqrt(4)

Yes.

There are of course lots of answers, many of them different - when I did this puzzle, mine were slightly different :-

1=4/4 * 4/4

2=4/4 + 4/4

3=(4+4+4)/4

4=((4-4)*4)) + 4

5=sqrt(4) + sqrt(4) + 4/4

6=4 + ((4+4)/4)

7=4 + 4 - 4/4

8=(4+4) * 4/4

9=4 + 4 + 4/4

10=sqrt(4) + sqrt(4) + sqrt(4) + 4

I believe that 5 and 10 are the only two numbers which -require- using square roots, but correct me if I'm wrong!

5= (4/4+4)*4

10=(44-4)*4

Post a Comment

<< Home