NPR Sunday Puzzle (Jun 24, 2012): The Cat is Away

NPR Sunday Puzzle (Jun 24, 2012): The Cat is Away:

Since I'm not going to be around to comment on the puzzle, I'm putting this week's puzzle on "auto-pilot". Please play nicely and don't give the puzzle answer away.

Here's my standard reminder... don't post the answer or any hints that could lead directly to the answer (e.g. via Google or Bing) before the deadline of Thursday at 3pm ET. If you know the answer, click the link and submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't give the answer away. You can openly discuss your hints and the answer after the Thursday deadline. Thank you.

Edit: From my comment, We just reached our destination (goal line). After the family got settled here inside... (go all in)

A: GO ALL IN + E --> GOAL LINE

NPR Sunday Puzzle (Jun 17, 2012): Est-ce que tu parles français?

NPR Sunday Puzzle (Jun 17, 2012): Est-ce que tu parles français?:

Q: Think of a common French word that everyone knows. Add a "v" (as in "violin") to the beginning and an "e" at the end. The result will be the English-language equivalent of the French word. What is it?

Well, I never expected it to take me this long to figure out the puzzle answer. I spent much of last night pouring through lists of common French words as well as English words starting with V and ending with E. My wife was similarly stymied so we gave up and assumed that there must be a typo in the wording of the puzzle. Unfortunately, when I listened to the on-air puzzle, the wording was the same as what is posted. Perhaps it was the clearer head of the morning, but I finally figured out what Will wanted us to do.

It's actually refreshing, for a change, to have a puzzle that takes some time to solve, but I expect there will be some that want to voice a small complaint when the answer is revealed especially since you may find me guilty of not giving a very obvious clue either.

Edit: I think I was actually rather generous with the hints this time:

"Well, I never expected" --> initial letters spell WINE

"pouring" --> deliberate misspelling of poring, as in pouring WINE

"wife + typo" --> WINE

"clearer head of the morning" --> no personal experience with this, but...

"what Will wanted" --> string of words starting with W

"refreshing" --> another indirect hint to a beverage, coupled with France = WINE

"takes some time" --> as in aging a fine WINE

"voice a small complaint" --> WHINE

"Find Me Guilty" --> Movie starring VIN Diesel

"giving" --> hides the word VIN

The key for me was actually listening to the on-air puzzle and hearing Will say the puzzle was tricky. But what finally caused the "Aha!" moment was searching for the puzzle submitter "Kate MacDonald" "Murphys, California" and finding her listed as the Winemaker of Stevenot Winery in Murphys, California. In the end this puzzle was challenging but not impossible.

A: French word: VIN, English word: WINE (VV = W)

GeekDad Puzzle of the Week: When Are the Odds Even?

GeekDad Puzzle of the Week: When Are the Odds Even?:

Q: If we have a bag containing equal numbers of black and white marbles, and we pull out one marble, the odds of it being black are even. If we have a bag containing 120 marbles, 85 of which are black, the odds of us pulling out two marbles and them both being black is also even — (85/120)x(84/119) = 0.5 or 50%.

If the largest bag we have can hold 1,000,000 marbles, for how many sets of marbles (i.e., the 120 marbles described above are one set) can we pull two marbles and have a 50% chance of them being the same designated color? Are there any sets of marbles for which we can pull three marbles and have a 50% chance of them being the same designated color? If so, how many?

After the solution is revealed, I'll post the details of my answer.

Edit: GeekDad Puzzle Solution:
In the first case you are essentially looking for integer solutions to:
a(a-1) = 2b(b-1)

There are EIGHT sets under 1 million that will result in even odds when 2 balls are drawn.

4 marbles (3 black) --> 4 x 3 = 2(3 x 2)
21 marbles (15 black) --> 21 x 20 = 2(15 x 14)
120 marbles (85 black) --> 120 x 119 = 2(85 x 84)
697 marbles (493 black) --> 697 x 696 = 2(493 x 492)
4,060 marbles (2,871 black) --> 4,060 x 4,059 = 2(2,871 x 2,870)
23,661 marbles (16,731 black) --> 23,661 x 23,660 = 2(16,731 x 16,730)
137,904 marbles (97,513 black) --> 137,904 x 137,903 = 2(97,513 x 97,512)
803,761 marbles (568,345 black) --> 803,761 x 803,760 = 2(568,345 x 568,344)

Interestingly, the next number in each sequence can be computed as follows:
a(n) = 6a(n-1) - a(n-2) - 2

So for example, the next numbers in the sequence would be:
Total balls: 6 x 803,761 - 137,904 - 2 = 4,684,660 marbles
Black balls: 6 x 568,345 - 97,513 - 2 = 3,312,555 black

Integer sequences: A011900 and A046090

In the second case you are looking for integer solutions to:
a(a-1)(a-2) = 2b(b-1)(b-2)

There is only ONE set under 1 million that will result in even odds when 3 balls are drawn.

6 marbles (5 black) --> 6 x 5 x 4 = 2(5 x 4 x 3)

NPR Sunday Puzzle (Jun 10, 2012): Have a Seat

NPR Sunday Puzzle (Jun 10, 2012): Have a Seat:

Q: Name something to sit on. Divide the letters of this exactly in half. Move the second half to the front, without changing the order of any letters. The result will name some things seen on computers. What are they?

Add the letters D-E-M to the answer, rearrange to name something that might be affected the longer you sit on one of these.

Edit: BARSTOOL + DEM --> BLOODSTREAM

A: BARSTOOL --> TOOLBARS

NPR Sunday Puzzle (Jun 3, 2012): Stay Tuned

NPR Sunday Puzzle (Jun 3, 2012): Stay Tuned:

Q: Take the names of two state capitals. Change one letter in each one, resulting in a phrase naming someone you will see soon on TV. Who is it? (Hint: You don't really have to know anything about TV to solve this puzzle.)

Whenever I wade through the channels to see what is on TV, I see nothing but re-runs.

Edit: My hint was "wade" which is a hint to the states of WA and DE as well as an indirect hint to water and diving.

A: Olympic Diver
Olympia, WA --> Olympic
Dover, DE --> Diver

GeekDad Puzzle of the Week: Waffle Cuts

GeekDad Puzzle of the Week: Waffle Cuts:

Q: If we only cut along the ridges of a circular waffle, and if each cut traverses the waffle in a straight line from edge to edge, how many different ways can the waffle be cut?
Note: rotations, horizontal flips, and vertical flips of a set of cuts should only be counted once.

Given that there are 6 places to cut vertically and 6 places to cut horizontally, that's a total of 12 cut lines. If you allow for any combination of these 12 lines to be cut or not, you have a total of 2^12 = 4096 ways to divide the waffle. But of course, the puzzle asks for the number of unique ways to cut the waffle, not including any mirrored or rotationally symmetric sets of cuts.

After the official answer to the puzzle is posted, I'll post my solution here.

Edit: The solution is posted, but just the number without any detail. Also, I disagree with their counting of the "no cuts at all" solution as one of the ways to "cut" the waffle. In any case, a full detailing of my solution along with an enumeration of all 665 (or 666) ways to uniquely cut the waffle can be found in Blaine's Solution to the GeekDad Waffle Puzzle.