Car Talk Puzzler: Lost Wages in Vegas

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MarleysGh0st · #1 Post by **MarleysGh0st** » Mon Mar 03, 2008 2:14 pm

I haven't posted one of these in a while. I like it when they have mathematical puzzles like this one. I bet Kazoo likes them, too!

RAY: This is from my Lost Wages series and it was sent in by Katherine Curtis. She writes, "A man is visiting Las Vegas, known for gambling casinos and the like, and he falls for the local hype and heads for a casino with hopes of hitting it big. He goes into this unusual casino that charges a dollar to enter, as well as a dollar to leave. He pays his dollar, plays the slot machines, loses half his money and in disgust pays his one dollar and leaves.

"The following day he knows he'll do better. He takes the money he has left and heads out to the same casino. He pays his buck, but just like before, he again loses half his money, and pays another dollar to leave.

"On the third day he figures he'll give it one more shot but his money is dwindling fast. The same thing happens. After paying his one dollar entrance, he loses half his money, and then pays his last dollar to get out. He's flat broke when he leaves."

So the question very simply is, how much money did he start with?

If you want to send your answer to Car Talk, you can use this link:
http://www.cartalk.com/ct/3500.jsp

TheConfessor · #2 Post by **TheConfessor** » Mon Mar 03, 2008 2:32 pm

Seems pretty straightforward to me, but those are famous last words, so I'll probably get this wrong. I just did this quickly in my head and it seems like he must have started with

Spoiler

21 dollars

Is that right?

MarleysGh0st · #3 Post by **MarleysGh0st** » Mon Mar 03, 2008 2:40 pm

That's the same answer I came up with.

Greyhound Dude · #4 Post by **Greyhound Dude** » Mon Mar 03, 2008 3:47 pm

Spoiler

I calculated his starting "funds" as $21.

earendel · #5 Post by **earendel** » Tue Mar 04, 2008 6:07 am

MarleysGh0st wrote:I haven't posted one of these in a while. I like it when they have mathematical puzzles like this one. I bet Kazoo likes them, too!

RAY: This is from my Lost Wages series and it was sent in by Katherine Curtis. She writes, "A man is visiting Las Vegas, known for gambling casinos and the like, and he falls for the local hype and heads for a casino with hopes of hitting it big. He goes into this unusual casino that charges a dollar to enter, as well as a dollar to leave. He pays his dollar, plays the slot machines, loses half his money and in disgust pays his one dollar and leaves.

"The following day he knows he'll do better. He takes the money he has left and heads out to the same casino. He pays his buck, but just like before, he again loses half his money, and pays another dollar to leave.

"On the third day he figures he'll give it one more shot but his money is dwindling fast. The same thing happens. After paying his one dollar entrance, he loses half his money, and then pays his last dollar to get out. He's flat broke when he leaves."

So the question very simply is, how much money did he start with?
If you want to send your answer to Car Talk, you can use this link:
http://www.cartalk.com/ct/3500.jsp

I hope this doesn't turn out like the "golden apples" Puzzler of a couple years ago.

andrewjackson · #6 Post by **andrewjackson** » Tue Mar 04, 2008 7:50 am

Spoiler

Gotta be $21.

Ends up with zero.
Exit fee - $1
Gambling loss - $1
Entry Fee - $1

Started day 3 with $3

Exit fee - $1
Gambling loss - $4
Entry fee - $1

Started day 2 with $9

Exit fee - $1
Gambling loss - $10
Entry fee - $1

Started day 1 with $21

kusch · #7 Post by **kusch** » Tue Mar 04, 2008 8:14 am

Spoiler

Hope I did this spoiler right. How can it be $21? If he lost 1/2 his money on day one would that amount not be $10.50 not $10? I understand where the starting amount could be $21.00 but...........

And no, I do not have an answer just curious where do you start the 1/2 thingie.

MarleysGh0st · #8 Post by **MarleysGh0st** » Tue Mar 04, 2008 8:21 am

kusch wrote:
Spoiler
Hope I did this spoiler right. How can it be $21? If he lost 1/2 his money on day one would that amount not be $10.50 not $10? I understand where the starting amount could be $21.00 but...........

And no, I do not have an answer just curious where do you start the 1/2 thingie.

Spoiler

I've been waiting for someone to question that!

The wording of the question is open to debate, but the way I interpret that (and the others who answer apparently agree) is that they're saying he loses half the money he has after he pays the $1 entrance fee.

andrewjackson · #9 Post by **andrewjackson** » Tue Mar 04, 2008 8:54 am

kusch wrote:
Spoiler
Hope I did this spoiler right. How can it be $21? If he lost 1/2 his money on day one would that amount not be $10.50 not $10? I understand where the starting amount could be $21.00 but...........

And no, I do not have an answer just curious where do you start the 1/2 thingie.

Spoiler

OK, if you take it as he loses half the money he started the day with, the answer is $28.

Day 1, start with $28.

Entrance fee: $1
Gambling loss: $14
Exit fee: $1

Ends first day with $12

Day 2, start with $12

Entrance fee: $1
Gambling loss: $6
Exit fee: $1

Ends second day with $4

Day 3, start with $4

Entrance fee: $1
Gambling loss: $2
Exit fee: $1

Ends third day with zero.

I still think $21 is a better interpretation of the question.

VAdame · #10 Post by **VAdame** » Tue Mar 04, 2008 9:29 am

Spoiler

I calculate $21.

He had $3 on Day 3, plus the dollar had had to pay for leaving the casino on Day 2. That equals $4, which was "half his money" on Day 2. Plus the dollar to get in. So, Day 2 started out w/ $9. Plus the dollar exit fee on Day 1 = $10. 2 x 10 = 20 + the dollar entrance fee on Day 1 = $21.

WWTBAM Bored

Car Talk Puzzler: Lost Wages in Vegas

Car Talk Puzzler: Lost Wages in Vegas

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