Fun math problem that stumps everyone

[38Chevy454]

How about another fun math question?
For a long trip, I bring engine coolant and distilled water in case I have to refill.
The specification is to mix 50% engine coolant and 50% distilled water.
I don't want to bring measuring cup.
So, how do I get exact 50% engine coolant and 50% distilled water on the road?

Easy answer: buy 2 gallons of premixed "ready to use" coolant. Also BTW, depending on your climate you may not need a full 50% coolant, but that's a different question.

 

[38Chevy454]

This reminds me of a math question related to investment volatility/beta I saw years ago.

On the first trading day of the new year, you invest exactly $10,000 in a stock .
It goes up 90% the 1st year, & down 50% the following year.
Are you ahead or behind ?

You weren't supposed to use a calculator. I cheated.

Behind, by 5%. Leave money out of it, just use starting with 100%, then after first year 90% increase it is 190%. Down 50% (half) the second year leaves 95% remaining, or 5% behind where you were at the beginning two years prior.

 

[Dtail]

Behind, by 5%. Leave money out of it, just use starting with 100%, then after first year 90% increase it is 190%. Down 50% (half) the second year leaves 95% remaining, or 5% behind where you were at the beginning two years prior.

Umm this was an easy one.

 

[freedom2022]

I use two same size transparent empty bottles of Gatorade.
Fill one full with coolant. Divide it to the other bottle until the two show the same level of liquid inside.
Then, top up the bottle with distilled water.

 

[Out-to-Lunch]

To me, the non-mathematician, "The driver averaged 30 mph for the first mile" is the same as saying "The one-mile trip took 2 minutes."

Are you sure you aren't a mathematician?

 

[RobbieB]

Her's my fav;

Three guys rent a room together at a motel, the clerk collects $30, 10 bucks each.

Then he realizes he over charged the guys, it was a $25 special, so he gives the bell hop $5 and says please refund this to those guys.

The bellhop thinks those guys will be happy with anything so he gives them 1 dollar each and keeps 2 dollars for himself, which means they now paid nine dollars each.

So 3 guys paid nine dollars each for $27 total and the bell hop has $2. What happened to the other dollar?

 

[NW-Bound]

So 3 guys paid nine dollars each for $27 total and the bell hop has $2. What happened to the other dollar?

No, the above accounting is wrong.

It should be this. Three guys paid $9 each for a total of $27. The bell hop kept $2, and the hotel got $25.

$27 = $2 + $25.

There's nothing missing.

PS. CFOs who do accounting like the above puzzle get long jail terms when caught.

 

[NW-Bound]

Back to the original puzzle about an average speed, here's a related real life situation.

We know that speed radars cannot catch local motorists who know where the speed traps are and slow down when driving past them. Hence, I read that in Germany they have a clever way to defeat it.

They use a camera to read the license plate of each passing car. Then, a few kilometers further down the highway, a second camera reads the license plates again. A computer divides the distance by the elapsed time between the camera capture instances. And that's the motorist average speed.

If he does not maintain a constant speed, then his top speed will be a lot higher than this computed average speed. However, the fine is just levied on the average speed, which cannot be disputed.

 

[RobbieB]

No, the above accounting is wrong.

It should be this. Three guys paid $9 each for a total of $27. The bell hop kept $2, and the hotel got $25.

$27 = $2 + $25.

There's nothing missing.

PS. CFOs who do accounting like the above puzzle get long jail terms when caught.

Yeah, you just can't do the math that way -

 

[Amethyst]

After all is done, the guests have $3.00 ($1 each).
The bell hop has $2.
The clerk has $25.
It all adds up to $30.

If the bell hop hadn't stolen $2.00, each guest would have paid 1/3 of $25, or $8.44 cents (plus a penny from one guest).

Her's my fav;

Three guys rent a room together at a motel, the clerk collects $30, 10 bucks each.

Then he realizes he over charged the guys, it was a $25 special, so he gives the bell hop $5 and says please refund this to those guys.

The bellhop thinks those guys will be happy with anything so he gives them 1 dollar each and keeps 2 dollars for himself, which means they now paid nine dollars each.

So 3 guys paid nine dollars each for $27 total and the bell hop has $2. What happened to the other dollar?

 

[ERD50]

Back to the original puzzle about an average speed, here's a related real life situation.

We know that speed radars cannot catch local motorists who know where the speed traps are and slow down when driving past them. Hence, I read that in Germany they have a clever way to defeat it.

They use a camera to read the license plate of each passing car. Then, a few kilometers further down the highway, a second camera reads the license plates again. A computer divides the distance by the elapsed time between the camera capture instances. And that's the motorist average speed.

If he does not maintain a constant speed, then his top speed will be a lot higher than this computed average speed. However, the fine is just levied on the average speed, which cannot be disputed.

I'm surprised the IL tollway system doesn't do this. If you don't have an iPASS (the electronic tolling system), tolls are double, so regular users almost all have iPASS transponders. It would be child's play to take the timestamp from each point (which is already collected), and compare to the known minimum legal time between those points. Issue a ticket if the time is short.

I can imagine the "unforeseen consequences" (which I just foresaw!) would be that if you were in stop and go for half the distance, you'd drive +100 mph the rest of the way! Well, they might still have cops watching for the really obvious offenders.

As I understand it, they don't issue moving violations for these 'robotic' offenses (like red light camera violations). The legal challenge was that anyone could be driving the car, so you can't ticket the driver w/o pulling them over and getting ID, but you can fine the owner.

-ERD50

 

[RobbieB]

Yup.

25+5=30
30-5=27-2
(10-1)x3+2=29

 

[NW-Bound]

Two trains A and B are headed towards one another on the same track in a head-on collision.

They are initially 25 miles apart. Train A travels at 20 mph. Train B has the speed of 30 mph.

A bird C flies at the speed of 40 mph, starting at train A towards train B. Upon reaching B, it reverses direction and flies back towards A. Upon reaching A, it turns back towards B. This continues until the bird is squashed between the two trains.

From the start until the end, what is the total distance travelled by the bird?

 

[Out-to-Lunch]

Two trains A and B are headed towards one another on the same track in a head-on collision.

They are initially 25 miles apart. Train A travels at 20 mph. Train B has the speed of 30 mph.

A bird C flies at the speed of 40 mph, starting at train A towards train B. Upon reaching B, it reverses direction and flies back towards A. Upon reaching A, it turns back towards B. This continues until the bird is squashed between the two trains.

From the start until the end, what is the total distance travelled by the bird?

Ahh, shades of good ol' Johnny Von Neumann. https://news.ycombinator.com/item?id=1866783


Spoiler material is presented in white text:

from "The Legend of John Von Neumann" - http://stepanov.lk.net/mnemo/legende.html
'Then there is the famous fly puzzle. Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover ? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann; "all I did was sum the infinite series." '

 

[ERD50]

Two trains A and B are headed towards one another on the same track in a head-on collision.

They are initially 25 miles apart. Train A travels at 20 mph. Train B has the speed of 30 mph.

A bird C flies at the speed of 40 mph, starting at train A towards train B. Upon reaching B, it reverses direction and flies back towards A. Upon reaching A, it turns back towards B. This continues until the bird is squashed between the two trains.

From the start until the end, what is the total distance travelled by the bird?

I got that in less than a minute (and I'm tired, ready for bed), but the earlier question helped put my mind in the right spot. It's pretty simple when you think about the information given and break it down and avoid the obvious series of calculations.

It always makes me wonder how many times I've tried to solve something the hard way when there was a simple method - but no one presented it as a trick, so I didn;t go look for the 'trick'?

-ERD50

 

[NW-Bound]

A man did not have a watch, only a good clock. However, he let the clock's battery run down, and now he did not know the time to set it after replacing the battery. He did not have a phone to call his friend a few blocks away to ask for the time.

He walked over to visit his friend and spent an evening. He then walked back home and set his clock accurately.

How did our man do this, as he would need to know how long the walk took?

 

[Koolau]

Back to the original puzzle about an average speed, here's a related real life situation.

We know that speed radars cannot catch local motorists who know where the speed traps are and slow down when driving past them. Hence, I read that in Germany they have a clever way to defeat it.

They use a camera to read the license plate of each passing car. Then, a few kilometers further down the highway, a second camera reads the license plates again. A computer divides the distance by the elapsed time between the camera capture instances. And that's the motorist average speed.

If he does not maintain a constant speed, then his top speed will be a lot higher than this computed average speed. However, the fine is just levied on the average speed, which cannot be disputed.

Yeah, and folks think I'm paranoid about GPS, OBD and cell phones. See my tag line - again. YMMV

 

[ERD50]

Yeah, and folks think I'm paranoid about GPS, OBD and cell phones. See my tag line - again. YMMV

Anything which can be used can be misused. Anything which can be misused will be

In what way is that misusing the technology? We have speed limits, this is a technological solution to enforcement. Sounds good to me. Catch those speeders, make them pay! All without a cop having to risk his/her life on a traffic stop.

Seems all good to me.

-ERD50

 

[Amethyst]

By no means! But I did hang with a few of them, so something could have rubbed off.

Are you sure you aren't a mathematician?

 

[Amethyst]

It's a poor engineer who declares the job done without proposing ways to apply light speed to the operational solution. I demand to see your morphological box.

Mathematically, light speed is still not a solution.

But to an engineer, that's close enough.

 

[ERD50]

A man did not have a watch, only a good clock. However, he let the clock's battery run down, and now he did not know the time to set it after replacing the battery. He did not have a phone to call his friend a few blocks away to ask for the time.

He walked over to visit his friend and spent an evening. He then walked back home and set his clock accurately.

How did our man do this, as he would need to know how long the walk took?

Is the part I bolded an intentional red herring? Would he "need to know how long the walk took"?

You state the clock is battery powered. so could he have simply carried it to his friend's house and set the clock there? But... you infer he set it when he got home, so I assume that's out-of-bounds.

One solution I could think of is finding when sunset, or moon-rise, or some celestial body appeared in the sky, and setting the clock according to that.

A less satisfying solution is that he could have counted the seconds to walk to his friend's house, so would also know how long it took to walk back. I guess both have a fair degree of possible error.

-ERD50

 

[ERD50]

It's a poor engineer who declares the job done without proposing ways to apply light speed to the operational solution. I demand to see your morphological box.

Or spherical chickens in a perfect vacuum, if you are a theoretical physicist.

-ERD50

 

[f35phixer]

seeing how this thread has tilted a little bit
here's another one...

You are in a room that is an 8x8x8 perfect cube. There are no windows, or doors (don't ask me how you got in there!) In the center of the floor there is a 12 inch pipe that is sticking 6 inches out of the floor. In the bottom of the pipe is a ping pong ball with a diameter that is one millimeter smaller than the inner diameter of the pipe. You have a 12 inch piece of string, a match, a magnifying glass, a 6" ruler and a paper clip. How do you get the ping pong ball out of the hole?

 

[ERD50]

Ahh, shades of good ol' Johnny Von Neumann. https://news.ycombinator.com/item?id=1866783


Spoiler material is presented in white text:

Don't put white text spoilers in a quote box!

The quote box is shaded, so the white text still shows up (a bit dim, but readable).

Here's white text in the main body (barely readable):

This is not a spoiler, unless you have very good eyes, or maybe a high contrast monitor?

But in a quote box....

This is a bit of a spoiler.

At least on my monitor/browser/settings.


-ERD50

 

[ERD50]

seeing how this thread has tilted a little bit
here's another one...

You are in a room that is an 8x8x8 perfect cube. There are no windows, or doors (don't ask me how you got in there!) In the center of the floor there is a 12 inch pipe that is sticking 6 inches out of the floor. In the bottom of the pipe is a ping pong ball with a diameter that is one millimeter smaller than the inner diameter of the pipe. You have a 12 inch piece of string, a match, a magnifying glass, a 6" ruler and a paper clip. How do you get the ping pong ball out of the hole?

The only thing I come up with, which is not very satisfying is to unbend the paper clip most of the way, with maybe a small hook at one end, and a loop at the other, just big enough to tie the string to.

I assume you can light the match? The magnifying glass would not help w/o sun through a window.

So light the match, heat the paper clip, guide it down the hole and hope you can manage to melt the ping-pong ball to get it to stick to the paper clip, and gently pull it out. Between the height of the ball, and the length of the paper clip, the 12" string should be enough to reach.

But that only gives you one try if you only have one match, so I dunno - sounds weak.

edit/add: Another weak solution: You didn't say the pipe was fixed in the ground, just "sticking out". Just pull it out, turn it upside down, and the ball falls out!


-ERD50