BrainDen.com - Brain Teasers

# joef1000

Members

32

1

2. ## An infinite amount of money?

So let's say I have a time machine, and I put £1,000 into a bank account (at time t=0). Now, if I don't touch it for a year (call this t=2), I'll have some interest on my original £1,000. Let's say the interest rate is 1% per year (works for any interest rate really). Then at t=2, my balance is £1,010. So if I ask to withdraw all my money, so I now have £1,010 in my wallet. Then I use my time machine to travel to the day after I deposited the original £1,000, call this t=1,and deposit half the money in my wallet, that is, £505. I then go back to t=3, where I still have the other £505 in my wallet. BUT... If I deposited the money, then at t=1 I had £1,505, instead of £1,000. So at t=2, adding 1% interest gives me £1,520.05, so THAT'S actually how much I withdraw. So I deposited half of that = £560.02 and kept £560.02 for myself at t=3 (I'll give the extra penny to charity) But that's more money, which means it actually become more, and more, and more. Does it converge, or do I have a truly infinite supply? Can we increase our final outcome if the initial parameters change? Let's go to the maths! Let M be the amount of money I have (since all my money at any given point is either in the bank or in my wallet, I only need one letter to denote this. M0 is my starting money at t=0, M1 is money at t=1, and so on. M0 = £1000 Let I be the interest rate, aka 0.01. Let P be the proportion of my money I deposit at t=1 (the rest I keep at t=3, giving the remainder to charity), this = 0.5. Equations: A. M1 = M0+P*M2 B. M2 = M1* 1 + I) C. M3 = (1-P)*M2 Substituting A into B gives M2 = (M0+P*M2)*(1+I) M2/(1+I) = M0+P*M2 M2/(1+I)-P*M2 = M0 M2*(1/(1+I)) - M2*P = M0 M2 * (1/(1+I)-P) = M0 M2 = M0 / (1/(1+I) - P) So the amount we end up with at then end (M3) is 1-P ------------- * M0 1/(1+I) - P If 1-P > 1/(1+I)-P, we made a profit. 1 + I > 1 -> 1 / (1+I) < 1 -> 1 / (1+I) - P < 1-P We made a profit. How much profit? If it's more than I, this was worth it. Let's plug in our values: (1 - 0.5) / (1/1.01 - 0.5) = 1.0202020202... ​We (slightly more than) doubled the interest rate. In fact, changing the interest rate with P = 0.5 doubles the interest rate What about different values of P (putting depositing more at t=1)? Lower values of P end up giving results close to 1.01, but higher values give more profit: for example, (1 - 0.9) / (1 / 1.01 - 0.9) 1.11, effectively bumping up the interest rate to 11%. However, going too high gives negatives, so what's the highest point we can go to? Answer: P = 1/1.01 = 100/101. Then our money goes to infinity. (as we divide by 0) So for interest rate I, depositing (1/(1+I)) of the money at t=1 when in the past means you end up with an infinite amount. Of course, due to rounding, you can't deposit exactly this amount, but you get more money each "iteration" so you can round it more accurately each time. And if you give the remainder of division after rounding to charity, you'd be helping infinitely too. (in most cases) The only limit is the amount of money your wallet can carry at once as you travel through time.
3. ## Chuck Norris Jokes

Chuck Norris' keyboard has two buttons: 0 and 1 Chuck Norris' computer can solve the halting problem Chuck Norris has counted to aleph one. Twice. Chuck Norris can count the real numbers Chuck Norris knows all of pi Chuck Norris's computer never crashes because it is afraid to Chuck Norris doesn't need antivirus, viruses are afraid to enter his computer Chuck Norris can type sudo rm -rf / --no-preserve-root without crashing his computer When Chuck Norris uses sudo, there are less privileges Chuck Norris can delete system32 without his computer crashing Chuck Norris's computer can execute an infinite loop in 2 seconds Chuck Norris catch 'em all, shiny Chuck Norris can go back in time, kill his grandfather, and still live Chuck Norris can run Windows fast Chuck Norris can see the source code of all binaries Chuck Norris can break a one time pad Chuck Norris can decrypt RSA with a public key Bill Gates, Steve Jobs, and Linus Torvalds live in constant fear that Chuck Norris' computer will crash Chuck Norris can construct a set of all sets that don't contain themselves Global Warming exists because Chuck Norris turned the sun up
4. ## Ways to Annoy your Roommate

Put windows on their computer
5. ## Obscure Jokes

Loops should start at 0.
6. ## The wish game

In this game, you have to make a wish, whilst corrupting the wish above you. Inspired by the same game on another forum here. There are rules: - No wishing for more wishes - No wishing for more than one thing in a wish (although a wish can have as much detail as you like) - No wishing to break these rules - When you corrupt a wish the corruption must be related to the wish, for example if someone wishes for a cookie you can't say "Granted, but you die before receiving it" because that has nothing to do with the wish itself, you could, however, say "Granted but it's poisoned and you will die if you eat it". - Make sure what you say Example: Person1: I wish for a sandwich. Person2: Granted, but it's a dirt sandwich. I wish for a book. Peerson3: Granted but it's boring. I wish for a 3DS. ...and so on. Feel free to be as creative as you like in the wishes and corruptions! I'll start: I wish for a bar of chocolate.
7. ## What is better - eternal bliss or a simple bread?

The word 'nothing' has two different meanings: the zero value, or no value at all. This paradox arises from confusing those two things. In symbols: (where > means "is better than") ¬((¬∃x(x > eternal-bliss) ∧ bread > 0) -> bread > eternal-bliss)

1) For the bullet to penetrate anything, it must have the majority of the energy in the universe. Likewise for the armour that nothing can get through; it must have the majority of the energy. There can't be two majorities. 2) Either it is the fountain of youth which stops ageing but does not prevent death by accidents such as drowning, so yes, or it is prevents all death, so no. 3) I don't accept it. Oh, look, I completed it. Do I get credit anyway? 4) My resolutions to this temporal paradox: a) The universe implodes b) It is in a separate timeline distinct from the original but identical in every way up to the time travel but diverges them, any action there would not affect her as she came from this universe, they would only affect the girl in the other universe. c) The laws of probability will warp as she gets close to killing her grandmother so that normally improbable events will occur more to ultimately prevent her from killing her d) She ends up not being born but then is spontaneously called into existence with all the memories she would have had had she been born, specifically to use the time machine and kill her grandmother, then ceases to exist moments after. 5) Which is why weather people who say it will be twice as cold or twice as hot are stupid 6) It won't be. 7) Your car will cease to exist before reaching the speed of light as all it's matter will be converted to energy 8) Proof of the nonexistance of god. QED.
9. ## Evil Genies

Granted, it crashes into YOUR house and kills you. I wish for a new phone with lots of memory.
10. ## How Many Were Going To Saint Ives?

1 or 2801. It's all down to interpretation of who's going TO st Ives and who's coming FROM st ives.
11. ## Evil Genies

Granted. There's no air so you can't breathe. I wish for an expensive car that does NOT fall out of the sky onto my head, simply appears in my garage, AND it is ready to drive, fuel and all, AND I don't crash it.
12. ## Evil Genies

granted, but not intended by you, intended by me. So the wish kills you. I wish i could never die, neither could my closest friends, and i don't get tortured forever. and my friends never end up hating me.
13. ## Evil Genies

Granted, but it's oblivion so you die I wish the world doesn't end
14. ## It seems to be hard!

It's the position in the alphabet divided by 2
15. ## Evil Genies

Granted, but I was forced to ungrant your wish as the magic in the granting would have crashed the server forever. I wish 1+1=3
16. ## The elusive chord

My above solution assumes that you define random in a way that makes all chord lengths equally likely. (I hate the edit system on this site)

18. ## Evil Genies

I wish this topic was not over and continues
19. ## Evil Genies

Therefore you un-granted it. That means you failed to grant his wish so you broke the genie rules. And, since you didn't grant it, you can't of corrupted it. Therefore it is the un-corruptible wish and phil1882 is the rightful winner unless someone can find a way to corrupt his wish.
20. ## Evil Genies

Granted, but the granting of my next wish results in the non-granting of your wish. I wish this wish was incorruptible.
21. ## Evil Genies

granted, but even though you know how to, you are incapable of doing so. I wish this wish is not corrupted

3) queueing
23. ## Evil Genies

granted, but you electrocute yourself just after figuring out what it's for I wish for a machine that will make whatever i want 100% of the time and it always works and doesn't blow up and cannot be stolen for it is too heavy to lift.
24. ## Evil Genies

Granted, but that makes the post so long that it crashes the site's servers and now no-one can get brain teasers and it's all your fault. (this reminds me of a similar game on another forum http://scratch.mit.e...opic.php?id=281) I wish the forum in the link I just gave was not going to close at the end of the year
25. ## Try to figure this out

A guy walks a mile south from his camp to collect some resources, when suddenly, HE WAS ATTACKED BY A BEAR!!!!! Quickly, he ran 1 mile west to get to safety. "Phew! That was close!", he thought. So he walked a mile north back to his camp. Question: What colour was the bear?
×

• #### Activity

• Riddles
×
• Create New...