Solution To: Four Fours

Here is the original problem:

Four Fours

How many numbers can you represent using four 4's and any available operation?

For example, here is the representation for the number 0:

0 = 44 - 44

See how the representation contains four 4's

Find the representation for the numbers 1 through 10.

Solution:

This problem is an interesting problem in that there isn't just one solution.  Here is the solution that one person gave:

1 = (4/4)+4-4 2 = (4*4)/(4+4) 3 = (4+4+4)/4 4 = ((4-4)/4)+4 5 = ((4*4)+4)/4 6 = ((4+4)/4)+4 7 = 4+4-(4/4) 8 = 4+4+4-4 9 = 4+4+(4/4) 10 = (44-4)/4   And while her answer is correct, it isn't an the only correct solution.  For example the number one could also be represented in this way:  1 = (4+4)/(4+4) (and there are other solutions).  2 could be represented in this way: 2 = (4/4)+(4/4).  You see where I am going with this.  There are in fact many solutions to this problem.   Sincerely, The Math Freak