Re: Problem 320
- --- In firstname.lastname@example.org, clooneman@y... wrote:
>2.7027027.... being very close to e.
> But if the addends could contain a decimal part, then they would
> equal n/d, and you'd have:
> 2.7027027....*2.7027027....*2.7027027....*2.7027027.... (37 times)
> = 2.7027027....^37 = 9 474 061 716 781 832.651871822612603, as
> P.S. Only one problem with my answer if n/d is an integer, because
> using 36 integers (three less 2s and two more 3's) yields 5 856 458
> 868 470 016. Whoops....
> P.P.S. And repeating that step again gets you a bigger product
Each new line is the previous divided by 8 and multiplied by 9.
>But interestingly, two 2's and thirty-two 3's gets youduh. Because 2+2=4?
> exactly the same result as when you shrink the number of integers
> 1 and use thirty-two 3's and one 4! Anyone see why?
This is interesting. When I did this problem before, I always used
rationals for addends. Rational addends close to e always gave the
best results. So when Peter used natural numbers for addends, I
thought they must be 3's and 2's because they are closest to e. Now
you are showing that using a 4 can give the same result. Four is not
very close to e.
I can add e 36.7879.. times.
Can I multiply e 36.7879.. times?
- --- In email@example.com, "cooperpuzzles"
>More importantly 2x2=4
> --- In firstname.lastname@example.org, clooneman@y... wrote:
> duh. Because 2+2=4?
> This is interesting. When I did this problem before, I always usednot very close to e.
> rationals for addends. Rational addends close to e always gave the
> best results. So when Peter used natural numbers for addends, I
> thought they must be 3's and 2's because they are closest to e. Now
> you are showing that using a 4 can give the same result. Four is
The addends must be 2 or 3, not because they are closer to e, but
because an alternative to the addend 5, is the addends 2 and 3 which
have a product of 6, which is greater than 5
similarly 4 x 2 > 6, but 3x3 is even bigger.
5x5 >10 and 3x3x4 is even bigger, because I showed above you would
not use the addend 5.
6x5>11, but you can do better than a 6 and a 5.
so all addends greater than 4 would never be used.
4 only gets a run because 2x2=4
by using 4 you don't get a higher product, merely a smaller number
[count] of addends.