You have created a 19 digit number with your 20 digit tiles as follows:

7_340_46_2010_51_49

Unfortunately someone knocked out 5 of the number tiles and placed them with the remaining number tile. The 6 tiles that are out are 6 3 2 8 9 3.

Without using any calculators, programs, or similar devices, what is the easiest way to figure out what the probability that my original 19-digit number will be a perfect square and what is this probability?

Note: The pesky "someone" also renumbered the number tiles so they were wrong and you couldn't tell what the right numbers are. This has been fixed to make the problem easier.

(In reply to with a computer (or a table of squares) by Charlie)

you say: "This has probability 1/2 of happening" etc

Not true. The 5 tuple belonging to the original number is
either
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.

Too tired to do it- leave it to others

ady

Posted by Ady TZIDON on 2004-03-23 18:02:28