k-man

Welcome to the forum, Trackcoach. It's impossible to make a schedule that would satisfy ALL of your requirements. Something needs to change. For example, you should be able to do it in 6 weeks, but not in 5. Here is why... Given that there are 10 teams and every team must meet every other team exactly once there should be a total of 45 head-to-head events. To fit it in 5 weeks you would need to hold 9 events every week. The only way to do that is to have 3 teams compete in one location (one host and 2 guests) and do it in 3 locations. This will require one team to get a buy every week. So far, so good. The problem is that the team that gets a buy will only compete in 4 remaining weeks and can therefore see only 8 other teams, but it needs to see 9. If you allow 4 teams to meet in one location (albeit not all 4 get to compete with all others at that time) then you should be able to do it in 5 weeks. Hope this helps.

never mind...

So, we're solving for flat triangles formed by coins in 3d space?

Well, if overlapping is not allowed then...

if the computer correctly predicts your picking style, then whatever money is disclosed in the envelopes is payment to your uncle. If the computer incorrectly guesses your picking style then whatever is disclosed in the envelopes is your payment. So option B So, the amount won or lost is determined by the contents of both envelopes in all cases? I was assuming that only the chosen envelope determines the amount.

What a great puzzle!!!

Is the short stick (1ft) rotating around the long stick (2ft) with the 1RPM speed relative to the long stick or to the stationary yardstick?

While that's a good observation, it's not strictly a requirement.

I see my mistake now and agree too. The expected winnings should be 50 cents in both cases.

Yeah, but It took me a while to find it...

The small circle makes a full revolution when the point p is in the same orientation as before, not when point p touches the large circle again.