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.
posted by steven | 9:11 AM
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
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