IBM Research | Ponder This | January 2010 solutions

# Ponder This

## January 2010

<<December January February>>

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