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Deleted member 8579
Enlightened
- Apr 28, 2021
- 1,323
That's what you have to do, otherwise you don't know if you've actually solved it.I'm too lazy to check 14 is the only ambiguous sum of possible ages.
It is easy when you are given the hint to use Bertrand. You solved it correctly, although you used different intervals than I did (my solution is in reply 27).Seems pretty easy
you just partition numbers between 10^n and 10^(n+1) into
the intervals:
[10^n, 2*10^n], [2*10^n+1, 4*10^n+2], and then [4*10^n+3,10^(n+1)]
then you just have to show 10^(n+1) > 8*10^n+6 which holds when n>0. and you have
your proof from Bertrand's postulate.