January 2010
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We received dozens of nice solutions (many thanks to our innovative solvers).
Some we did not accept, like using the rounding function: ceil(sqrt((2*2)!)).
If we allow for the constant e, then we can have ln(ln(e)/ln(sqrt(sqrt(sqrt(sqrt(sqrt(e))))))/ln(2). But allowing for any constant makes the problem too easy, since we can trivially get 5=(i+i+i+i+i)/i. That's why we did not accept the nice solution (2+i)*(2-i). Using esoteric functions we can get solutions like 2 + vercosin(arccos(2)).
You can get any integer by -log_2(log(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(exp(2))))))))).
As done sometimes by computer scientists, if we denote lg(x) as log_2(x) then lg(lg(2)/lg(sqrt(sqrt(sqrt(sqrt(sqrt(2))))))) is also a solution.
And a nice solution for 5 is cos(atan(2))^-2.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com