Fun Mathy Type Riddles

[vorlon13]

imagine this is an infinite grid of 1 ohm resistors




what resistance value will you measure across the one resistor highlighted there ??

(and note, while I remember the answer, I don't remember the math that yields it)

[downbeatplumb]

---

47

---

Oh yeah. When you say it like that its obvious.

---

https://www.youtube.com/watch?v=kf6-DQuo0Po

[Losty]

imagine this is an infinite grid of 1 ohm resistors




what resistance value will you measure across the one resistor highlighted there ??

(and note, while I remember the answer, I don't remember the math that yields it)

Wut

[vorlon13]

it's from sparky school !!

[brewer]

This can be approached as a mathy puzzle or one can work like a dog with some pretty ugly fractions.  (Don't be that guy.)

There are two glasses containing an equal volume, one of milk and one of grape juice.  A spoonful of grape juice is taken from its glass and stirred into milk glass.  Then a spoonful of what had started as pure milk is returned to the grape juice glass and stirred in.  At the end of each such cycle the two glasses again contain exactly the same volume of liquid.  The process is repeated some number of times.  When finished will there be more grape juice in the milk glass or more milk in the grape juice glass or ..?

---

If each glass only contained one spoonful each, then it does not matter how many cycles. Remember this comes from a math tard cheater.

---

[brewer]

This can be approached as a mathy puzzle or one can work like a dog with some pretty ugly fractions.  (Don't be that guy.)

There are two glasses containing an equal volume, one of milk and one of grape juice.  A spoonful of grape juice is taken from its glass and stirred into milk glass.  Then a spoonful of what had started as pure milk is returned to the grape juice glass and stirred in.  At the end of each such cycle the two glasses again contain exactly the same volume of liquid.  The process is repeated some number of times.  When finished will there be more grape juice in the milk glass or more milk in the grape juice glass or ..?

---

If each glass only contained one spoonful each, then it does not matter how many cycles. Remember this comes from a math tard cheater.

---

Nobody responded.

---

Is the answer that it will be unequal until at least half the volume is exchanged, and then equal after that?

---

[Whateverist]

This can be approached as a mathy puzzle or one can work like a dog with some pretty ugly fractions.  (Don't be that guy.)

There are two glasses containing an equal volume, one of milk and one of grape juice.  A spoonful of grape juice is taken from its glass and stirred into milk glass.  Then a spoonful of what had started as pure milk is returned to the grape juice glass and stirred in.  At the end of each such cycle the two glasses again contain exactly the same volume of liquid.  The process is repeated some number of times.  When finished will there be more grape juice in the milk glass or more milk in the grape juice glass or ..?

---

If each glass only contained one spoonful each, then it does not matter how many cycles. Remember this comes from a math tard cheater.

---

Sorry I've spent the day outside choking on the smokey air.

---

It is a special case but the answer is the same in every other case too. Interestingly, even if you began with exactly one spoonful in each glass the answer will be the same, namely "the same amount of each contaminant in each glass". In this case there would be 50% of each liquid in each glass, but that doesn't affect the answer. As F&F said, the quantity of liquid in each glass is the same in each glass at the end of each cycle. So however much is missing from the grape juice is not in the milk glass, and exactly that much milk can only then go into the grape juice glass.

---

---

---

If each glass only contained one spoonful each, then it does not matter how many cycles. Remember this comes from a math tard cheater.

---

Nobody responded.

---

Is the answer that it will be unequal until at least half the volume is exchanged, and then equal after that?

---

---

So long as complete cycles are completed in the manner specified it will be equal after each and every cycle .. no matter the size of the glass, the spoon or the number of cycles.

---

[brewer]

---

If each glass only contained one spoonful each, then it does not matter how many cycles. Remember this comes from a math tard cheater.

---

Sorry I've spent the day outside choking on the smokey air.

---

It is a special case but the answer is the same in every other case too.  Interestingly, even if you began with exactly one spoonful in each glass the answer will be the same, namely "the same amount of each contaminant in each glass".  In this case there would be 50% of each liquid in each glass, but that doesn't affect the answer.  As F&F said, the quantity of liquid in each glass is the same in each glass at the end of each cycle.  So however much is missing from the grape juice is not in the milk glass, and exactly that much milk can only then go into the grape juice glass.

---

---

Nobody responded.

---

Is the answer that it will be unequal until at least half the volume is exchanged, and then equal after that?

---

---

So long as complete cycles are completed in the manner specified it will be equal after each and every cycle .. no matter the size of the glass, the spoon or the number of cycles.

---

---

Sorry, that makes no sense to me. After you transfer one spoonful of juice to the milk, stir, then transfer back one spoonful of juice/milk to the juice you're replacing a minute amount of juice back to the juice and transferring a lesser minute amount of milk. The concentrations will not be exactly the same, only the volume will. 

---

Please ignore my crankiness.

Edit: NVM, fog lifted.

[FatAndFaithless]

Moar riddles plz.

[Whateverist]

---

Sorry, that makes no sense to me. After you transfer one spoonful of juice to the milk, stir, then transfer back one spoonful of juice/milk to the juice you're replacing a minute amount of juice back to the juice and transferring a lesser minute amount of milk. The concentrations will not be exactly the same, only the volume will. 

---

Please ignore my crankiness.

Edit: NVM, fog lifted.

Hey, we're both entitled. Enjoy an occasional crank myself. Just in case ..

---

.. anyone else is still caught up in that dilemma, here is another way to look at it.

After some number of cycles the GJ glass contains some amount "m" of milk and the rest is GJ. That means the milk glass is missing "m" amount of milk. Yet the glasses contain an equal volume of liquid. That means the missing amount of milk (m) must have been replaced with exactly m amount of GJ. So the two glasses contain the same amount of contaminant and the same amount of starting liquid.

---