4 ms·
>The system only has 25^5 states Not true. The problem is in one-to-one correspondence with the non-negative solutions to a + b + c + d + e = 25 which is in
by gragas 9y ago
>The system only has 25^5 states
Not true. The problem is in one-to-one correspondence with the non-negative solutions to
a + b + c + d + e = 25
which is in one-to-one correspondence with the positive solutions to
a + b + c + d + e = 30
which is a simple counting problem---(29 choose 4) = 23751.
In my opinion, you should really try to prove your math to yourself before answering with such an authoritative tone.
- jordigh 9y agoI guess what sounds authoritative is that I'm using jargon while trying to explain the jargon at the same time, as if I knew what I was talking about. I've since edited my comment. I know it's stars and bars, but I keep messing up the count. Anyway, it's a finite amount, it's not huge, and your count is wrong too by a sister comment. :-)
- gragas 9y agoI agree with your point. :-) Why is my solution incorrect, though? * Oh, I see why my solution is wrong. It's never the case that one person has all the money. I should take some of my own advice.
- jensv 9y agoCounting is just very difficult. You can easily be off by orders of magnitude and not even recognize it.
- Retric 9y agoOne player can't get all the money as they have to hand out a dollar every turn and they can't receive all the money on the same turn. 23751 - 5 = 23746