Thursday, July 31, 2008

NPR Sunday Puzzle (Jul 27): Egomaniac Anagram

NPR Sunday Puzzle (Jul 27): Egomaniac Anagram:
Q: Re-arrange the letters in the word 'egomaniac' to spell a sign seen in many stores. What is it?
Well we have returned home from Iceland safely. One thing I will say, is if you try and pronounce the place names, you'll find most Icelanders replying, "what did you say?". A pronounciation hint -- the town of "Höfn" sounds like a hiccup. The 'fn' is pronounced 'b' so don't say "Hoffin", say "Hub" as you inhale quickly. As for the puzzle, it's so easy, you can solve it faster than you can say, Kirkjubæjarklaustur (trust me, don't try...).

Edit: There were a couple hints above -- returning to a place, and the phrase "What did you say?". I initially thought that there would be a gerund with "ing" so I pulled those letters aside. I then saw the word "come" in the remaining letters and knew the answer.

Friday, July 25, 2008

Friday Fun - How Long is the Ring Road around Iceland? - Answer

We should be flying back home from Iceland about this time. Hopefully everyone has had fun with the puzzles while we have been gone. If you haven't had a chance to solve the puzzle about the Iceland Ring Road yet, take a look at last Friday's post and don't read any further. But if you want the answer, read on...
A: Let A be the speed of the first couple and B be the speed of the second couple. After an equivalent amount of time T, one couple has traveled AT miles and the other travels BT miles. For the return, the first couple now travels BT miles in 9 hours, while the other couple travels AT miles in 16 hours.

A = BT/9
B = AT/16

9A = BT
16B = AT

T = 9A/B
T = 16B/A
9A^2 = 16B^2
Take the square root of both sides (which is okay because both are positive)
3A = 4B

This tells us the ratio of their speeds is 4 to 3. In other words, over the same time, the faster couple will travel 4/7 of the ring road, the slower couple will travel 3/7. The difference is 120 miles. And if 1/7 is 120 miles, the whole road is 840 miles.

Thursday, July 24, 2008

NPR Sunday Puzzle (Jul 20): Weekend Edition Sunday Puzzle -- Answer

We are still in Iceland so I this will have to be another "autopost". Since I didn't see the puzzle beforehand, I'm not sure how I managed to get some hints in there, but the following words do seem to be clues, at least to a possible answer:
Fruitful, Central, Dead(line)

Sunday, July 20, 2008

NPR Sunday Puzzle (Jul 20): Weekend Edition Sunday Puzzle

Well, this is an interesting post. I'm on vacation, so I'm actually still not around to be able to tell you what the puzzle is or to give you any hints.
Q: What is the answer to the puzzle on the NPR Website?
My wife and I should be in Akureyri in Northern Iceland at this point. We are planning on doing a whale-watching trip. I think we'll need to bundle up because it can get nippy out on the water watching whales frolick. If I'm lucky, that will be a fruitful clue to this week's puzzle and be central to solving it, but I doubt it. Help each other out, but don't give away the puzzle until after the dead line on Thursday 3pm ET.

Friday, July 18, 2008

Friday Fun - How Long is the Ring Road around Iceland?

My wife and I are taking a leisurely drive around Iceland on the Ring Road... at this point we should be a little more than half way on the East side of Iceland in Egilsstaðir. However, I thought it might be fun to give you a little topical puzzle in honor of our trip.
Q: Two couples leave Reykjavik at exactly the same time traveling opposite directions on the Ring Road around Iceland. When they meet later, one couple has traveled 120 miles farther than the other. After a night's rest in a hotel and some refueling, the couples continue their respective drives. The first couple arrives back at Reykjavik 9 hours later, the second couple takes 16 hours. Assuming that each couple maintains the same constant speed each time they drive, how long is the Ring Road around Iceland?
I'll post the answer next Friday.

Thursday, July 17, 2008

NPR Sunday Puzzle (Jul 13): Names from Early American History - Answer

My wife and I are away in Iceland for a couple weeks taking in the sights. At this point we should be in Höfn toward the Southeast of Iceland as part of an 11-day driving tour of the country. However, I didn't want to leave everyone wondering about the answer to the puzzle so I've provided a scheduled post to appear after the deadline... here it is:

Sunday, July 13, 2008

NPR Sunday Puzzle (Jul 13): Names from Early American History

NPR Sunday Puzzle (Jul 13): Names from Early American History:
Q: Name a famous person from early American history with five letters in the first name and five letters in the last. Six letters of the alphabet are used in this name, some of them repeated. These same six letters make up the name of another person in early American history whose first and last names have six and four letters, respectively. Who are these two people?
This wasn't too hard to figure out, but it might be helpful to have a list of names associated with early American history handy. Both names should be familiar to most people. One hint: don't assume that the names are exact anagrams of each other.

Friday, July 11, 2008

How old is Mark?

For everyone that struggled with the pencil puzzle, here's another algebra puzzle to "stretch your neurons". Pay attention...

The combined ages of Mark and Ann are forty-four years, and Mark is twice as old as Ann was when Mark was half as old as Ann will be when Ann is three times as old as Mark was when Mark was three times as old as Ann.

How old is Mark?

Thursday, July 10, 2008

NPR Sunday Puzzle (Jul 6): Contaminated Anagram

NPR Sunday Puzzle (Jul 6): Contaminated Anagram:
Q: Take the word 'contaminated.' Rearrange the 12 letters to get a two-word phrase for a familiar sign.
For all of you that complained that last week's puzzle was too hard, here's one that is extremely easy. A few minutes anagramming the letters will net you the answer (or you can cheat and use an anagram program). Feel free to leave a comment with a hint, but remember you aren't allowed to give any spoilers before the deadline of Thursday 3pm ET.

P.S. The answer isn't "Tandem Action". :-)

Edit: My hidden clue was "you aren't allowed...". I also liked phredp's clue in his comment about "I can't enter..." and geri's comment about "Admit it..."

Thursday, July 03, 2008

NPR Sunday Puzzle (Jun 29): Anyone have a Pencil?

NPR Sunday Puzzle (Jun 29): Anyone have a Pencil?:
Q: A man buys 20 pencils for 20 cents and gets three kinds of pencils in return. Some of the pencils cost 4 cents each, some are two for a penny and the rest are four for a penny. How many pencils of each type does the man get?
It's a rare NPR *math* puzzle. Using algebra you could write an equation for the number of pencils, and one for the cost of the pencils. But that results in two equations and three unknowns. Fortunately there are some constraints and a little trial and error will get you the answer. Note: You have to have at least one of each type, so just getting 4 of the first type and 16 of the last type wouldn't work.

Edit: I think the thing that confused most people was they assumed they had to buy 4 of the 1/4 cent pencils, or 2 of the 1/2 cent pencils. You can't make 20 cents with those constraints. Here's how I solved it.

Let A be the number of 4 cent pencils.
Let B be the number of 1/2 cent pencils.
Let C be the number of 1/4 cent pencils.

Number of pencils:
A + B + C = 20 pencils

Cost of pencils:
4A + B/2 + C/4 = 20 cents
Multiplying this second equation by 4 to remove the fractions we have:
16A + 2B + C = 80

Now subtract the first equation to eliminate one variable:
15A + B = 60

There are some obvious constraints on A. Because you need at least one of each type of pencil, none of the values can be 0. That eliminates A = 0 or A = 4. Trying the other values you get:
A = 1, B = 45 --> too many pencils
A = 2, B = 30 --> too many pencils
A = 3, B = 15 --> C = 2

3 pencils (at 4 cents) = 12 cents
15 pencils (at 1/2 cent) = 7 1/2 cents
2 pencils (at 1/4 cent) = 1/2 cent