Friday Puzzle -- Dinner plans

Re: Friday Puzzle -- Dinner plans

I have a guess, but I cannot make it because I have Triskadekaphobia.

No :-(

But the answer is much more straight-forward than you might think.

Re: Friday Puzzle -- Dinner plans

Considering that: Each person needs to sit next to 25 other people. He can sit next to two per night. The shortest possible time would be 13 nights - provided you can come up with an algorithm to generate 13 sequences that satisfy the 'never sat beside before' criteria.

But a strict applicaton of that requirement creates a problem: Each person needs to meet exactly 25 other people. At each seating, he/she will be seated between 2 people. After 12 seatings, an individual will have exactly one person left to meet. But the circular seating arrangement dictates that he/she will have to sit next to at least one 'old' friend.

Correct -- trick question ;-)

However... ;-)

Per the original question, people can be absent to get the answer. using this, you get 12 weeks to meet the first 25. Then, you can have weeks where everyone is absent except the two that need to meet. This will take 650 weeks (26 taken two at a time), so you could do it in 662 weeks or a bit over 55 years. This does take a bit of liberty with the "between" criteria.

Re: However... ;-)

Per the original question, people can be absent to get the answer.

That's what I get for trying to make the problem harder! As I originally saw it, it was 22 people, and no mention of possible absences. But this crew is too good, so I added the possible absences as a distraction.

using this, you get 12 weeks to meet the first 25.

Presuming you mean the first 24, I assume you are right. But the seating algorithm is not immediately obvious to me.

Then, you can have weeks where everyone is absent except the two that need to meet. This will take 650 weeks (26 taken two at a time), so you could do it in 662 weeks or a bit over 55 years.

I think you are over-complicating this case. If everyone has sat next to 24 others in the first 12 weeks, you have only 13 meetings to arrange, so only an additional 13 weeks of the two-person dinners.

This does take a bit of liberty with the "between" criteria.

Particularly the "two people" part of "between two people". ;-)