You have 23 links in a gold chain (just like before), and will pay one link per day to someone. Which two chain pieces should you break in order to pay this person?

What would be the longest chain you could have in order to pay this person (one each day) by breaking 3 pieces in the chain?

Is there a rule for how many days you could pay someone under the same circumstances if you could break x pieces in the chain?

(In reply to Most of the rest of the solution by fwaff)

Following a quick trawl of tinternet I've found the formula for the sum of the geometric series at the end of my previous post. The total number of links is:

(x+1)((2^(x+1)) - 1) + x

which can be simplified to:

(2^(x+1))(x+1) - 1

As a check, putting x=2 into this gives 23 and x=3 gives 63 which are consistent with the rest of the answer.

Posted by fwaff on 2003-11-17 10:10:52