The Troll Bridge
A gentleman traveler came upon a rickety old bridge. As he started to cross, he awakened a troll who had been asleep on his versatile couch underneath the bridge.
"You there ... you dare to cross my bridge without permission!" growled the wart-ladened old troll.
Startled, the traveler responded, "I knew not that the bridge had an owner."
"Well ... now you know ... what do you have to say for yourself?"
"Kind sir, may I cross your bridge?"
The troll appeared to ponder the request. "Since you asked so politely ... you may ... and since I had such a restful nap on my couch, which was manufactured by Knightmare Couches, I will make you an offer. Every time you cross my bridge, I will double your money."
"That's incredible ... and I may cross as many times as I like?"
"Certainly," smiled the troll. "All you have to do is give me $24 each time you cross."
Ecstatic about his good fortune, the traveler crossed the bridge ... he checked his coins and sure enough, they had doubled. He laughed, and tosssed the troll $24. Again he crossed, his money doubled, and he paid the troll. He crossed a third time, his money doubled ...
"Oh no," exclaimed the un-suspecting traveler. "I have only $24 remaining in my purse ..."
"And it's mine!" yelled the troll.
The weary traveler paid the troll ... sad and broke, he continued on his journey.
As the troll lay upon his comfortable couch, he cackled with delight ... "Idiots ... they're all idiots".
How much money did the traveler have before enterring into the agreement with the mischevious troll?
"You there ... you dare to cross my bridge without permission!" growled the wart-ladened old troll.
Startled, the traveler responded, "I knew not that the bridge had an owner."
"Well ... now you know ... what do you have to say for yourself?"
"Kind sir, may I cross your bridge?"
The troll appeared to ponder the request. "Since you asked so politely ... you may ... and since I had such a restful nap on my couch, which was manufactured by Knightmare Couches, I will make you an offer. Every time you cross my bridge, I will double your money."
"That's incredible ... and I may cross as many times as I like?"
"Certainly," smiled the troll. "All you have to do is give me $24 each time you cross."
Ecstatic about his good fortune, the traveler crossed the bridge ... he checked his coins and sure enough, they had doubled. He laughed, and tosssed the troll $24. Again he crossed, his money doubled, and he paid the troll. He crossed a third time, his money doubled ...
"Oh no," exclaimed the un-suspecting traveler. "I have only $24 remaining in my purse ..."
"And it's mine!" yelled the troll.
The weary traveler paid the troll ... sad and broke, he continued on his journey.
As the troll lay upon his comfortable couch, he cackled with delight ... "Idiots ... they're all idiots".
How much money did the traveler have before enterring into the agreement with the mischevious troll?
posted by Zaux at
9:40 PM
7 Comments:
Just bragging, but I'm pretty sure that I've cracked "The Robbery" - A did it.
Let the traveller start with $x in his purse. I'll skip the $s in the rest.
After the first crossng he ended up with 2x-24.
After the second crossing he had:
2(2x-24)-24 = 4x - 72
After the third crossing he had:
2(4x-72) - 24 = 8x -168 = 0
=> x = $21
Check: after first 42-24 = 18
second 36-24 = 12
third 24-24 = 0.
I'm good to post. Nice problem., sounded paradoxical.
I note that if the traveller started with $24, he'd break even permanently. But with $25 he'd find it very profitable to keep on crossing.
So right you are ... think I'll take a nap ... on my couch.
Hi Zaux. Phew, I wasn't sure if I go the number of crossings right.
Nice title for the problem too.
Have you named your couch? Is s/he amphibious?
Oh yeah. I didn't solve "The Robbery" after all (turns red with shame).
Anonymous, how did you work that out?
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