99 Pirates

Reply #5

lakerben — Wed, 26 Apr 2023 03:20:22 GMT

Interesting.

Reply #4

GreyhoundTips — Thu, 06 Apr 2023 20:37:48 GMT

Hello cottoneyedjoe

Sorry if I used this thread to get in touch with you, but I could not send you a private message nor I could post on an old thread that you had.

I read a post from you called Lottery Bible generator program. I have been studying some numerology and astrology and would like to apply that knowledge for selecting winning numbers.

Could you kindly send me a copy of your program?

If you have time, we could discuss authors and astronumerological theories.

Reply #3

cottoneyedjoe — Thu, 09 Mar 2023 16:07:23 GMT

There's another version of this problem where there are an odd number of pirates ( 20, say) and the chest cannot be opened unless a majority are present. For example, if there were 9 pirates, then the solution is 9 choose 5 = 126 locks. 11 pirates and 462 locks, 13 pirates and 1716 locks, 15 pirates and 6435 locks, 17 pirates and 24310 locks, etc.

Reply #2

db101 — Wed, 08 Mar 2023 17:25:20 GMT

There is no smaller solution, LOL.

Reply #1

cottoneyedjoe — Wed, 01 Mar 2023 20:06:16 GMT

The smallest solution I could find is that the treasure chest is shut with 156,849 locks and each pirate holds 4,753 non-duplicate keys.

The statement of the problem is equivalent to The chest cannot be opened if and only if three or more pirates are missing. This means there could be one lock for each size-three subset of the 99 pirates. Each pirate in that trio should hold a key to that lock. Since 99 choose 3 = 156849, that is the number of locks required. Each pirate is a member of 98 ch... [ More ]

99 Pirates

db101 — Sun, 26 Feb 2023 21:14:03 GMT

99 pirates collectively own a treasure chest. They want to put enough locks on it so that the treasure chest can be opened if and only if there are at least 97 of the 99 pirates present. How many different locks do they need to put on the chest and how many different keys does each pirate need to keep in his possession