# Car Talk's puzzle of the week: impossible?

I generally try to solve Car Talk’s weekly puzzler, but this week’s has baffled me. I’m sure I must have missed something.

Here, stripped of all their obfuscation, is what I understand the puzzle to be:

Six coins (presumably modern American currency) together have a value of \$1.15. You cannot take two or more coins to equal the following sums:
\$1.00
\$0.95
\$0.50
\$0.25
\$0.10
\$0.05

If I understand the puzzle correctly, I think the following things are true:

1. You can’t have more than 1 50-cent piece, because then you could make change for \$1.00.
2. You can’t have more than 1 quarter, because then you could make change for \$0.50.
3. You can’t have more than 1 dime, because if you had 2 dimes, you could subtract those two from the \$1.15 total and make change for \$0.95.
4. You can’t have more than 1 nickel, because then you could make change for \$0.10.
5. You can’t have any pennies, because the sum is a multiple of 5, and if you have 5 pennies, you could make change for \$0.05.
6. You can’t have any dollar coins, because if you do, it’s impossible to reach \$1.15 with 6 coins.
7. If you have the maximum number of each coin (zero dollar coins, 1 fifty-cent piece, 1 quarter, 1 dime, 1 nickel, zero pennies), you’ve got \$0.90 with 4 coins.

My question goes out to two groups of people. Car Talk listeners, did I misunderstand some piece of the puzzle? Non-car-talk listeners, did I screw up my reasoning above?

I definitely don’t want anyone to tell me the answer to the puzzle, but if you can tell me what I misheard about the puzzle, that’d be awesome. Or if you can see a way to solve it using the clues above, just tell me it’s possible.

That’s what I heard too - don’t know how to solve it (yet?).

Never mind

I think I solved it. I’ll put it in a spoiler.

4 dimes, a quarter, and a 50 cent piece

Doesn’t work. A fifty cent piece, a quarter and two dimes makes ninety five cents.

I concur with LHoD’s analyis. I’m completely stumped.

Ah. Did the puzzle specify we’re talking about american denominations?

You’re right.

I’m pretty sure this is impossible.

Think I’ve figured it out - but it’s a hinky solution

[SPOILER]A dollar coin, and 5 3-cent pieces (which once were minted, and are probably still legal tender)

[/SPOILER]

Here’s the exact question on there website.

http://www.cartalk.com/content/no-change-ray-0?question

This seems to be what the OP posted. Although they didn’t specify that they’re American coins. They also didn’t specify the dates on the coins. Weren’t there some coins in the past worth other amounts?

I believe we have a winner.

I think that’s it.

Bo-o-o-o-o-o-o-o-o-o-o-o-gus!

Haven’t heard this week’s show, and don’t have an answer, but just have to say it was a real treat to hear my name out of the blue on the show once a while back when they used a puzzle suggestion I had sent in some months before

I’ve never seen a vending machine take half-dollars. Or is that just part of the obfuscation?

But can you put a 50c piece in a vending machine?

ETA: Ninja’d!

Ah–this is an interesting point. The exact exchange is,

I think that’s the part I was missing. If that’s the key to the puzzle–that it’s a quarter, a 50-cent piece, and four dimes, but that he couldn’t buy the candy bar because vending machines don’t take 50-cent-pieces, then it’s not a bogus puzzle at all.

Glad to see it was something I missed in the puzzle!

Now the one they had a few weeks ago, about the traveling salesman getting second-floor hotel rooms, that was bogus.

Do you have a link to the puzzle? Sounds neat.

I just submitted an answer on the website. It would be funny if one of us won after the OP pointed the puzzle out to us.