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?

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..."

A: CONTAMINATED <--> NO ADMITTANCE

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

A:
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

Catch That Bus!

The local bus leaves Ashwood at 9:21 am and arrives in Baytree at 12:06 pm on the same day. The express bus leaves Ashwood at 10:00 am, traveling the same route, and arrives in Baytree at 11:40 am. At what time does the express bus pass the local bus if each is traveling at a constant speed?

NPR Sunday Puzzle (Jun 22): Who are these TV personalities?

NPR Sunday Puzzle (Jun 22): Who are these TV personalities?

Q: Think of a famous TV personality whose last name has six letters. Drop the last letter, reverse the order of the remaining five letters, and you will get the name of another famous TV personality. Who are they?

I was all set with my answer of Johnny Carson and Oscar the Grouch until I reviewed my answer and discovered I didn't answer the question correctly. By the way, both names are last names.

Edit: Clues "reviewed" and "didn't answer the question correctly"

A: Who are Alex TREBEK and Roger EBERT?
(Correctly phrased in the form of a question...)

NPR Sunday Puzzle (Jun 15): English Tea Anagram

NPR Sunday Puzzle (Jun 15): English Tea Anagram:

Q: Rearrange the letters of ENGLISH TEA to name a famous person with a prominent mustache — first and last. Who is it?

I had a couple thoughts when approaching this puzzle. I first thought that the person must have some relevance to today, being it is Father's Day. My second thought was that the person might have been in the news recently; Will Shortz often does that (for example Harrison Ford was the subject of a puzzle around the time Indiana Jones IV was being released). Well, I don't think either of these things apply... or do they?
My hints: The person is a man. And there is only one L and one T available in the letters, so don't misspell his name.

Edit: The main clue was "Today"... and there were lots of good clues in the comments about being "critical", mentions of "onions", etc.

A: GENE SHALIT

NPR Sunday Puzzle (Jun 8): 5-Digit Sequence

NPR Sunday Puzzle (Jun 8): 5-Digit Sequence:

Q: A calculator displays a five-digit number. The first four digits are 8735. These digits form a logical sequence. What is the fifth number in the series?

I was led down the wrong path initially because I didn't read the puzzle carefully. There's an important clue in the question which you'll see if you are bright.


Edit: The key to the puzzle was to realize that these digits were on a calculator. I mentioned that in my clue along with the additional hints of "LED", "see" and "bright". I mentioned the word "segment" in one of my comments too.

A: The next digit is also 5. Each digit is the number of LED/LCD segments that are lit in the prior digit.

Guess this Social Security Number

A certain Social Security Number has the following qualities:

• It uses each of the digits 1 to 9 exactly once (with no zero).
• The digits from 1 to 2 (inclusive) add up to 12.
• The digits from 2 to 3 (inclusive) add up to 23.
• The digits from 3 to 4 (inclusive) add up to 34.
• The digits from 4 to 5 (inclusive) add up to 45.
• The digit 3 is NOT next to a dash (XXX-XX-XXXX).

What is this unique Social Security Number?

NPR Sunday Puzzle (Jun 1): Movie Star Synonyms

NPR Sunday Puzzle (Jun 1): Movie Start Synonyms:

Q: Name a famous male movie star. Change the first letter of his first name to a G and change the last letter of his last name to a T. The result will be two words that are synonyms. Who is the movie star and what are the words?

The first time I tried to figure this out I was little lost, but at last, after 3 or 4 attempts, the answer was completely clear.

Edit: It was crystal clear...

A: HARRISON FORD --> GARRISON, FORT
Click the link for Harrison Ford's first uncredited movie role (yes, that's the extent of it) as the bellhop.

NPR Sunday Puzzle (May 25): I.O.U. a clue

NPR Sunday Puzzle (May 25): I.O.U. a clue:

Q: The phrases 'part time' and 'time share' are familiar phrases with 'time' in them, and the adjoining words, 'part' and 'share,' are synonyms. Find two phrases that work similarly with the word 'child.' What are they?

Even with an extra day over the long weekend and I wasn't able to figure this one out yet. I have a couple answers where the words don't seem like strong synonyms, so I don't think either is the answer. One has 4 letter words for both parts. The other has words that start with the same letter. This week I'm hoping the commenters will come up with good clues in my place.

A: The accepted answers are up on the NPR website. Personally I have issues with all of them so I won't transcribe them here.