(In reply to re: with a computer (or a table of squares)
by Ady TZIDON)
<<you say: "This has probability 1/2 of happening" etc
Not true. The 5 tuple belonging to the original number is
8 5 4 7 2 or
8 5 4 5 2 or
8 5 5 7 2
All that out of "digits sum" consideration.
The prob. of the hundreds digit being even need to be evaluated for each of the cases along with the 5-tuples prob. as well. >>
Your possibilities are based on the number being a square. The probability I gave of the 100's position being even was in general, not based on it's being a square. The probability was 1/2, as each of the 6 tiles was equally likely to have come from the 100's position (again, disregarding whether the number is a square or not), and half the digits are even. My calculation of the square probability, based on that alone, was then computed based on the necessity of the 100's position to be even in order to produce a square.
Posted by Charlie
on 2004-03-23 20:58:57