bonanova

FM (GI) (19) ( L_ _ _ _ _ _ _ _ _ O_F _ _ _ _ _ _S ) DYHTPS? (13) M, IABGN (9) ( H_ _ _ _ _ _ _Y )

Clue: M E R G E R S E T E R N A L R E _ _ T _ _ G R _ _ I _ _ E N T I _ _ _ R A _ _ _ E _ S L _ _ _ _ S

Clues: OTIHIS, LSTH. IGOLAG, BTTS. OWCBTS, FFTS. SHWW, BTTS. (18) ( _ _ _ _ _ _ _ _ T_H_A_N T_H_E _ _ _ ) CTIT, TN. ANOGSYFTBATS. YKIT, TN. YFFYLIAK, TT. (8) ( T _ _ _ _ _ _ _ )

How many days does each person contribute to the total project days? Individuals don't contribute to the project's time. A can do a project, alone, in a days, but a does not increase the time of a project. Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc.

SP is first with both solutions. Tylerbrooksmusic was first with the closed course solution Good job both.

You have the longest non-returning path. The returning path can be slightly longer. I'm not sure which order of 7 and 8 you are using, but I see one path that is too short to use. There are no (chess) Knight moves, like 7-5 and 2-8 (using the correct 7 8 labeling). If you are using the original 8 7 labeling you are not using knight moves, but too many 1-4 type moves. Clue for those still working on this the longest total length is 47.97, and from that you can get the distribution of city-city distances used, and work out the path. Try my next, harder puzzle just posted.

dm92 has it.

I owe it to the Den to post at least one of these without error. Possibly this one does that. Give the longest route (sequence of city numbers) that visits all the cities (a) not returning to starting city (sum of 7 distances - starting point matters) (b) returning to starting city (sum of 8 distances - starting point does not matter) This puzzle has more choices than the first one. Cities lie clockwise on the perimeter of a 6x6 square: 6--O------O-------+--------O |3 4 5| | | | | 4--+ + | | | | | | 2--O2 6O | | | | |1 8 7| 0--O-------+-------O-------O | | | | 0 2 4 6 +----+---+---+ |City| x | y | Distances: +----+---+---+ 8.485 1-5 3-7 | 1 | 0 | 0 | 7.211 2-5 3-6 3-8 4-7 | 2 | 0 | 2 | 6.325 1-4 1-6 2-7 4-8 5-8 | 3 | 0 | 6 | 6.000 1-3 1-7 2-6 3-5 5-7 | 4 | 2 | 6 | 5.656 4-6 | 5 | 6 | 6 | 4.472 2-4 2-8 | 6 | 6 | 2 | 4.000 1-8 2-3 4-5 5-6 | 7 | 6 | 0 | 2.828 6-8 | 8 | 4 | 0 | 2.000 1-2 3-4 6-7 7-8 +----+---+---+

BG has the longest (non-returning) path. I have marked the puzzle solved, but we still have the longest (closed-loop) path to determine. (Post solutions in terms of the corrected 7-8 numbering and corrected 6.325 distance.)

Xavier is correct on both counts. I've modified the OP. Square root of 40 is 6.325. Edit: both of these paths are just shy of optimal.

dm92 has the correct number. (just the wrong units.)

Good guess BG, but I found one a little longer. This is the correct open route. P.s. I think it's more challenging than finding the shortest route, which in this case is trivial. If people like this genre I will post another.

Assume a network of straight roads connects every pair of cities. I did not draw all the roads to keep the map uncluttered, but gave the distances. That may have been a source of confusion. Visit every city once and only once, using those roads. No trips to Disney World. Paths can cross.

Yes. But visit each city only once.

I'll wait to be surprised. Maybe i'm misreading the puzzle. I don't think you need population estimates; you need guilty estimates. You ask the probability someone is correctly charged. If no one in the population has in fact committed a crime, that probability is 0. If everyone in the population has in fact committed a crime, that probability is 1. If the OP says on average 2% of the population has committed a crime, then what is ... Etc., the question has an answer. But again maybe I don't understand the question at all.

on the left of the chart (committed the crime or innocent of the crime) tells you whether they are actually guilty or not. I think the chart says how effective the court is. I think we need info about the people. But maybe this puzzle will surprise me.

Enough with traveling salesman who hate long road trips. Mario Andretti has joined the team, and he loves to drive! His route today comprises eight towns, placed at the corners of an octagon. Here are their coordinates: Edit: 7 and 8 are labeled incorrectly. They should be switched. +---+-+-+ City x y +---+-+-+ 1 0 2 2 0 4 3 2 6 4 4 6 5 6 4 6 6 2 7 4 0 8 2 0 +---+-+-+ The inter-city distances, to save some calculations, are N-S and E-W distances of 6, along with four different diagonal distances of 2.828, 4.472, 5.657 and 6.083 6.325 If Mario begins driving at city 1 (coordinates 0 2) and drives until he has visited them all, how far will he be able to drive, and what city will he visit last? If his objective is to return to his hotel in City 1 after visiting the other cities, how long of a trip could he accomplish?

Can someone draw that family tree?

Presume it tells you "equals" as well.

I won't spoiler this cuz I think it's a good one for group solve. Highest (?) is 118. After that I'm sure the negative numbers come into play, but I don't know how.

I can see some patterns in the upper left corner. But they seem to run out of steam. This will be interesting to see what others find.