Substitute each capital letter in bold by a different base ten digit from 0 to 9, such that (TAU)^.BETA when rounded off to the nearest integer is equal to PI, and the absolute difference of (TAU)^.BETA and PI is the minimum. Each of A, P and T is nonzero.

Notes:

(i) PI does not represent the quantity π and, .BETA denotes a decimal fraction.

(ii) Relevant alphametic rules are applicable for this problem.

I modified my code slightly solve a more general problem where instead of TAU^(0.BETA) being restricted to values that fit the PI alphametic pattern I instead searched for all values where the digits of the rounded number TAU^(0.BETA) where digits not already taken by T,A,U,B, and E.  I then looked for a minimum among these values and found an even closer one.
it is
TAU=972 BETA=1597 thus
972^(0.1597)=3.00006250056
rounded this gives 3, which does not conflict with the 9,7,2,1, and 5 already used. 

Posted by Daniel on 2009-09-05 16:17:30