Wednesday, January 20, 2010

New York Devil

A man from New Jersey was complaining that he doesn't have enough money. A devil descended from the sky and offered a deal to this man:
"Feel all this cash you have in your wallet? I can double it every time you cross George Washington bridge from NY to NJ. However, when you cross the bridge in the other direction you have to pay the $8 toll."
The man quickly agreed, but was left without any cash after just four trips.
How much cash did he have to start with?

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

6 comments:

W said...

If we work backwards:

On the last trip, he must have had $8 coming back. Before that, when crossing, he must have had $4 which was doubled to $8.

Coming back the third time, he must have had $12 since $12 - $8 = $4 he had before going over the 4th time from NY to NJ.

So in going over the 3rd time from NY to NJ, he must have had $6 (that doubled to the $12).

Coming back from the 2nd time, he must have had $6 + $8 = $14.

And then, crossing over the 2nd time from NY to NJ, that means he must have had $14 / 2 = $7.

Coming back the 1st time, $7 + $8 = $15

And then crossing over the 1st time = $15 / 2 = $7.50.



Let's just double check to see if that makes sense.

1) 7.5 * 2 = 15 ; 15 - 8 = 7
2) 7 * 2 = 14 ; 14 - 8 = 6
3) 6 * 2 = 12 ; 12 - 8 = 4
4) 4 * 2 = 8 ; 8 - 8 = 0!

So he must have started out with $7.50 He should really have started with an amount > $8.

Maria said...

Or he should have done some math before jumping into a deal with the devil.
Bravo W!

New puzzle tomorrow.

Kim said...

Congratulations on the great article, Maria! http://www.boston.com/news/local/articles/2010/01/21/needhams_math_mom_inspires_children_parents_to_love_numbers/?page=full

Maria said...

Thank you, Kim. And thanks to everyone in the Family Puzzle Marathon community. You are the ones that make it all fun and cool.

Kim was referring to the article about TheMathMom in today's West edition of the Boston Globe.

Anonymous said...

Robin figured this one out. It has to be $15.00, because the man starts in NJ.
Trip #1: $15.00-8=$7.00, double it for the way back, and you get $14.
Trip #2: $14-8=$6.00, double it for the way back, and you get $12.
Trip #3: $12-8=$4.00, double it for the way back, and you get $8.
Trip #4: $8-$8 =$0, double it for the way back, and you get $0

Maria said...

Very impressive, Robin!
I was re-telling this puzzle to my kids yesterday, and you know how kids always ask the right questions. My son asked: "Where the man was starting hos journey from, NJ, right?" and I felt that there is a hole in the solution...
Robin must have has this child-like scientific curiosity. Welcome to the marathon! You get your first puzzle-point.

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