[EventHorizon]

You are approached by a man holding a strange looking box.

The box has 6 chambers numbered 1 through 6. Each chamber contains 1 token. Each chamber also has two buttons on it with labels A and B.

Button A will remove a token from the chamber and add two tokens to the next higher numbered chamber (if it exists).

Button B will remove a token from the chamber and swap the contents of the next two higher numbered chambers (if they exist).

Chamber 6 has an extra button, C, which will remove a token from chamber 6 and cause the box to magically produce a dollar's worth of gold.

If held down for 3 seconds, a button will perform its function repeatedly and instantaneously until there are no more tokens in the chamber (or up to an amount you are thinking of at that moment). Tokens will resize themselves so you don't need to worry about overcrowding a chamber. Any tampering with the machine beyond pressing the buttons will cause it to shrink out of existence.

The man wants to sell you the box for one trillion dollars. You happen to be able to take out the loan to buy it, but only though some shady people who'll kill you if you don't pay back the loan within 24 hours (they will leave you alone if you pay it back and they'll take gold).

Do you buy the box?

[Guest]

Misread OP. NM

Edited July 20, 2011 by Zweefer

[Guest]

You wind up with anything up to 2.85E+192 or 2 to the power of 636 times 10. We are talking so much money, you would have to cut it off at some reasonable amount to avoid a world wide gold crash.

Start with box two. Use A to leave 0 in box 2 and 3 in box 3. Use B on box 1 to switch 2 and 3. Use A once on box 2 to put 2 in box 3. Use A in box 3 to put 3 in box 4. Again for 5 in box 4, nothing in box 3. Use B in box 2 to switch them. Use A in box 3 to double it to 10 in box 4. Use B in box 2 to switch them. Have 10 in box 3, use A to have 2 in box 4. Use A in box 4 to have 3 in box 5, then 5 in box 5. Then use B in box 3 to keep switching and A in box 4 to keep doubling, wind up with 640 in box 4. Use A in box 4 to put 2 in box 5. Use A in box 5 to put 3 then 5 in box 6, then use B in box 4 and A in box 5 to keep doubling as much as you like. I would stop at 2 trillion, no need to be greedy.

[Guest]

You wind up with anything up to 2.85E+192 or 2 to the power of 636 times 10. We are talking so much money, you would have to cut it off at some reasonable amount to avoid a world wide gold crash.

Start with box two. Use A to leave 0 in box 2 and 3 in box 3. Use B on box 1 to switch 2 and 3. Use A once on box 2 to put 2 in box 3. Use A in box 3 to put 3 in box 4. Again for 5 in box 4, nothing in box 3. Use B in box 2 to switch them. Use A in box 3 to double it to 10 in box 4. Use B in box 2 to switch them. Have 10 in box 3, use A to have 2 in box 4. Use A in box 4 to have 3 in box 5, then 5 in box 5. Then use B in box 3 to keep switching and A in box 4 to keep doubling, wind up with 640 in box 4. Use A in box 4 to put 2 in box 5. Use A in box 5 to put 3 then 5 in box 6, then use B in box 4 and A in box 5 to keep doubling as much as you like. I would stop at 2 trillion, no need to be greedy.

Bingo... As per my calculations the maximum tokens at any point of time in chamber 6 will be equal to 10 multiplied by 2 to the power 1277... and that's huge... can i have that box maker's address???

[EventHorizon]

Nana7 and rasar619 have the question right (a trillion is an insignificant fraction compared to the potential gold from the box), but both are low on the maximum payout. And as for the time limit, 24 hours was much more than is needed...even to max out the box.

Here are two new questions...

1. What is the maximum amount of gold you could get out of the box? (in the form "5*(2^X)" dollars worth)

2. What is the shortest amount of time allowed to repay the debt that is still manageable? (Assume 1 second per button press, 3 seconds per button hold, and ignore any travel time)

(FYI, I know 1 but haven't thought about 2)

I did a bit of calculation of how much gold you could get, and it seems like you could get 2^1406 cubic meters of gold. The mass of which easily dwarfs that of the sun (let alone the mass of the known universe)

I could have made some errors... I wasn't too careful doing the calculations.

[Guest]

Nana7 and rasar619 have the question right (a trillion is an insignificant fraction compared to the potential gold from the box), but both are low on the maximum payout. And as for the time limit, 24 hours was much more than is needed...even to max out the box.

Here are two new questions...

1. What is the maximum amount of gold you could get out of the box? (in the form "5*(2^X)" dollars worth)

2. What is the shortest amount of time allowed to repay the debt that is still manageable? (Assume 1 second per button press, 3 seconds per button hold, and ignore any travel time)

(FYI, I know 1 but haven't thought about 2)

I did a bit of calculation of how much gold you could get, and it seems like you could get 2^1406 cubic meters of gold. The mass of which easily dwarfs that of the sun (let alone the mass of the known universe)

I could have made some errors... I wasn't too careful doing the calculations.

1. 5*(2^1278)