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

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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.

You could work through it, finding possible 19-digit numbers and square roots - but that wouldn't be quick, would it?

Posted by Iain on 2004-03-23 14:40:31