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Re^5: Multiplication digit persistenceby LanX (Saint) |
on Mar 28, 2019 at 16:52 UTC ( [id://1231820]=note: print w/replies, xml ) | Need Help?? |
I have a math degree and know if many cases even nowadays were "amateurs" find good solutions. Don't wanna go to much into details but in order to calculate the likelihood of a solution (which is not alien to number theory). You'd need to calculate the density of possible products of single digits numbers in a number range.(easily done with the sieve approach) Since the number of 11 step solutions becomes infinite by just adding more 1s it's probably not that unlikely to find a solution with several hundreds or thousands digits.* Otherwise you'd need to prove why it's impossible. ( Which could be done by showing that the density becomes 0)
Cheers Rolf
update*) or at least prove it's existence.
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