Conundrum: Primary Colors
You may want to use a map for this one…
Imagine the 2008 Republican primaries are over, and only four candidates won any states. (DC, which is not a state, went to Ron Paul.)
1. Mitt Romney won more states than any other candidate.
2. Rudy Giuliani’s states included Massachusetts and Washington.
3. John McCain won all of the states beginning with one particular letter, and only those states.
4. Fred Thompson’s states included New Mexico.
5. Strangely enough, no two bordering states went for the same candidate. (Four Corners does not count as a border.)
Who won in Michigan? How do you know?
UPDATE: Puzzle solved by David. See comments for solution.
October 16th, 2007 at 1:32 pm
Who won in Michigan? How do you know?
I don’t know why you’d need a map. Just look for the candidate most willing to sleep with the auto workers’ unions.
Tip to others: save the map image (or maybe a black and white one) and then open it in Microsoft Paint. Then use the “Fill with color” paint can icon to label various states in various colors.
I’ll work on it some more.
October 16th, 2007 at 2:03 pm
I looked in vain for a US map that would work in Microsoft Paint, and none were ideal (black and white, with borders that could be filled in a variety of colors). The best I could find is this one:
http://www.myvacationrentalsonline.com/images/united_states_map%5B1%5D.gif
The colors don’t translate well, but you if play with it you can create four distinct ones: black, white, blue, and gray. Which is really all you need.
I started with the John McCain clue and went through the alphabet. He doesn’t win very many states, but I should think he wins more than 2. Add that to the existing criteria, and you’ve eliminated all but two letters.
That’s really all the logic I can offer so far. I started at the Four Corners and am working my way eastward, but am having a hard time by the time I get to Missouri, which borders everything.
October 16th, 2007 at 4:04 pm
Using a paint program is a good idea, Neel. Other maps that might prove useful for that strategy can be found here and here.
October 20th, 2007 at 4:42 pm
I should point out that there are no tricks in this puzzle, aside from its apparent simplicity. It does not depend on a close reading of my wording, nor any arcane knowledge of new rules for the 2008 election. It is what it looks like it is.
But there is only one way to assign the fifty states to the four candidates to fit the five conditions stated in the puzzle. Can you find it?
October 20th, 2007 at 5:11 pm
I was doing fine until I realized that I’d made an incorrect assumption early on. Starting over does not appeal to me right now, so I’ll have to look at it later. Much later.
October 20th, 2007 at 8:24 pm
It’s Rudy Giuliani. The election results are shown in the link below, where red are Rudy Giuliani states, blue are Mitt Romney states, green are Fred Thompson states, and orange are John McCain states.
October 20th, 2007 at 8:38 pm
OK, that link didn’t work.
States won by John Mccain:
Ohio
Oklahoma
Oregon
States won by Rudy Guiliani:
Alabama
Arkansas
Iowa
Kansas
Kentucky
Maryland
Massachusetts
Michigan
Nevada
New Jersey
North Dakota
Virginia
Washington
Wyoming
States won by Fred Thompson:
California
Delaware
Florida
Illinois
Louisiana
Minnesota
Montana
Nebraska
New Hampshire
New Mexico
New York
Rhode Island
South Carolina
Tennessee
Utah
West Virginia
States won by Mitt Romney:
Alabama
Alaska
Arizona
Colorado
Connecticut
Georgia
Hawaii
Idaho
Indiana
Maine
Mississippi
Missouri
Pennsylvania
South Dakota
Vermont
Virginia
Wisconsin
October 20th, 2007 at 10:04 pm
RUDY GIULIANI is correct! David, my hat is off to you. This was an extremely difficult puzzle. I’d be curious to hear your process for solving it.
Neel, I feel your pain, but at least you’re out of your misery. Thanks for playing.
David, your solution is complete, except that you have two duplicate states and are missing two states. Giuliani won North Carolina, not Virginia. Romney won Texas, not Alabama. Still, I’m sure it was correct on your map, and the error was just in transcribing.
You may have reached the same conclusion using a different method than I used when creating the puzzle, but here’s one way that the solution can be demonstrated to be unique:
1. It has been proven that any map can be colored in with four colors with no two regions that share a border the same color, but that’s a maximum. Some maps can be filled in this way using only three colors.
The map of the United States can be filled in using three colors, except in two areas. Nevada and Kentucky are both landlocked and surrounded by an odd number of states. Those areas need four colors, meaning that McCain must have won at least one state in each of the two areas.
2. The only common initial letters in those regions are I and O. I is out, because Illinois borders two other I states. Therefore, McCain must have won Ohio and Oregon. The only other O state is Oklahoma. The rest of the map must be filled in using only three colors.
3. Utah and Wyoming share a border and therefore must be two different colors. Idaho and Colorado border both of these two states, and must therefore be the third color. Colorado borders New Mexico, a Thompson state. Idaho borders Washington, a Giuliani state. Therefore, Idaho and Colorado must be Romney states.
4. By the same logic, Missouri must be a Romney state, via Nebraska and Kansas.
5. By the same logic, Virginia must be a Romney state, via Kentucky and Tennessee.
6. By the same logic, Pennsylvania must be a Romney state, via West Virginia and Maryland.
7. New York borders a Giuliani state (Massachusetts) and a Romney state (Pennsylvania), and goes to Thompson.
8. New Jersey borders a Romney state (New York) and a Thompson state (Pennsylvania), and goes to Giuliani. By the same logic, Romney wins Vermont and Connecticut, and we can fill in most of the other states.
9. Thompson wins New Hampshire, Rhode Island, and Delaware.
10. Giuliani wins Maryland.
11. Thompson wins West Virginia.
12. Giuliani wins Kentucky.
13. Thompson wins Illinois and Tennessee.
14. Giuliani wins North Carolina, Arkansas, and Iowa. Romney wins Indiana.
15. Romney wins Georgia, Mississippi, Texas, and Wisconsin. Thompson wins Nebraska.
16. Thompson wins Minnesota. Romney wins South Dakota. Giuliani wins Alabama, Kansas, and Wyoming.
17. Giuliani wins North Dakota. Thompson wins Montana, Utah, Louisiana, South Carolina, and Florida.
18. Giuliani wins Nevada.
19. Romney wins Arizona.
20. Thompson wins California, giving him a total of 16 states. Romney only has 14.
21. In order to have more than Thompson, Romney needs at least three of the remaining four states. Michigan borders Indiana and Wisconsin, two states that Romney won. Therefore, Romney must have won Maine, Alaska, and Hawaii.
22. Michigan would give Thompson 17 states, the same as Romney. But Romney must end up with the most. Therefore, by process of elimination, Rudy Giuliani must have won in Michigan.
October 21st, 2007 at 12:09 am
My thought process to figure out the McCain states is pretty much the same as yours. From there, I picked a “three-cycle” of states, three states that all bordered one another. I used Illinois, Iowa, and Missouri, and gave them the arbitrary labels A, B, and C. From there, it was relatively simple to label the rest of the states – Wisconsin bordered Illinois and Iowa, so it was labeled C, Minnesota got label A, etc. Idaho and Colorado were both C states; since Idaho bordered Washington (a Giuliani state) and Colorado bordered New Mexico (a Thompson state), C states must go for Romney. Working eastward, New York became an A state which bordered Massachusetts, a known Giuliani state. Thus, A states went for Thompson, and B states went for Giuliani.
Using the method I described, you can fill in every state except for Michigan (borders Wisconsin, Indiana (both Romney), and Ohio (McCain)), Maine (borders New Hampshire, a Thompson state), Hawaii, and Alaska. Thompson has 16 states, Giuliani 13 states, Romney 14 states, and McCain 3 states. From there, I followed your logic.