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.

solution: the sum of all the digits mod 9 is 5, while
the only possible outcomes for a square are:

0,1,4, and 7.
therefore out of the 6 tiles either one of the fives or
a seven or a 4 are not a part of the original number

still a long way to go...............

ady
Edited on March 23, 2004, 5:50 pm

Posted by Ady TZIDON on 2004-03-23 17:38:43