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Squares Probability II (Posted on 2004-03-23) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Gamer    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: with a computer (or a table of squares) | Comment 12 of 15 |
(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

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