Fun math problem that stumps everyone

[dheb]

"If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?"

The trick to this question is that you have to cover the whole first mile at 30 mph. If instead it had asked, "If you travel at a speed of 30mph for 1 minute, how fast do you have to go in the second minute so you have an average speed of 60mph over the 2 mile stretch?" In that case, the answer would be 90 mph.

 

[Out-to-Lunch]

Years ago, when things were less expensive: 3 salesmen go to a hotel and decide to stay in the same room to save money. The price was $30, so each man paid $10. After they were in the room the desk clerk remembered they were having a special rate reduction this week and the price should have only been $25. So, he gives the bell hop 5 one dollar bills to take back to the men. On the way up the bell hop puts $2 in his pocket and gives the men $1 each back. So now each man has paid $9 each, that is $27, the bell hop stole $2. what happened to the other dollar since they paid $30 total to begin with?

See upthread: https://www.early-retirement.org/forums/f27/fun-math-problem-that-stumps-everyone-113785-3.html#post2764657

 

[Koolau]

Same guy who taught me Einstein's Special Theory of Relativity in Physics 200 gave the class this problem: (not really math, but what the heck)

A guy lives in the penthouse on the 100th floor of a building. Every morning, he gets in the elevator and rides down to street level. There he buys a NY Times and a cup of coffee. He drinks his coffee and reads the Times. When finished, he gets back on the elevator and rides up to the 50th floor where he exits and walks the remainder of floors to the 100th floor. (He is not an exercise nut.)

 

[NW-Bound]

Same guy who taught me Einstein's Special Theory of Relativity in Physics 200 gave the class this problem: (not really math, but what the heck)

A guy lives in the penthouse on the 100th floor of a building. Every morning, he gets in the elevator and rides down to street level. There he buys a NY Times and a cup of coffee. He drinks his coffee and reads the Times. When finished, he gets back on the elevator and rides up to the 50th floor where he exits and walks the remainder of floors to the 100th floor. (He is not an exercise nut.)

I read this riddle before. Will not spill the beans now.

 

[NW-Bound]

I have two coins in my pocket. They add up to 30 cents. One of them is not a nickel.

What coins do I have?

 

[Car-Guy]

^^^^
One is a quarter and one is a nickel. (you said "one" was not a nickel)

 

[REWahoo]

^ What's next, "Who is buried in Grant's tomb?"

 

[MichaelB]

^ What's next, "Who is buried in Grant's tomb?"

Well? Don’t keep us guessing …

 

[Archman]

I stumbled upon this simple looking math problem last week and showed it to several people and have not found anyone that got it right, including my daughters 6th grade math teacher. It took Albert Einstein an hour to figure it out.

If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?

90 mph Just basic algebra.

ave = (x + y)/2
60 = (30 +y)/2
120 = 30 + y
120-30 = y
90= y

 

[RobbieB]

Numbers is hard eh?

 

[Koolau]

Numbers is hard eh?

Reminds me of when "New Math" became popular (you'll have to click over to YouTube to watch)

 

[NW-Bound]

Two American Indians are sitting on a log. The little Indian is the son of the big Indian. However, the big Indian is not the father of the little Indian.

Explanation?

 

[ERD50]

90 mph Just basic algebra.

ave = (x + y)/2
60 = (30 +y)/2
120 = 30 + y
120-30 = y
90= y

You haven't read much of this thread, have you?

As I mentioned upstream, https://www.early-retirement.org/fo...-that-stumps-everyone-113785.html#post2764408

"This thread is a great example of "Thinking, Fast and Slow".

Your algebra itself is fine (fast thinking), but it doesn't apply to the problem in the OP (requires a bit of slow thinking). So your answer, based on basic algebra, is very wrong.

Two American Indians are sitting on a log. The little Indian is the son of the big Indian. However, the big Indian is not the father of the little Indian.

Explanation?

I heard this in the 70's but it was a car accident and a surgeon.

White text spoiler alert:

The big Indian, in a deep voice says: "I am not your Father, I am your Mother".

-ERD50

 

[RobbieB]

Mother

 

[RobbieB]

OK, how much dirt is in a hole in the ground 12 inches x 12 inches x 1 foot deep?

 

[Ronstar]

^ none

 

[ERD50]

OK, how much dirt is in a hole in the ground 12 inches x 12 inches x 1 foot deep?

Wait, is that a cylindrical hole, 12 inches diameter, or a square hole, 12" x 12"?

And why the switch from 12 inches to 1 foot - is that a trick?

OK, either way it's zero, but details are important (sometimes!).

-ERD50

 

[ERD50]

Same guy who taught me Einstein's Special Theory of Relativity in Physics 200 gave the class this problem: (not really math, but what the heck)

A guy lives in the penthouse on the 100th floor of a building. Every morning, he gets in the elevator and rides down to street level. There he buys a NY Times and a cup of coffee. He drinks his coffee and reads the Times. When finished, he gets back on the elevator and rides up to the 50th floor where he exits and walks the remainder of floors to the 100th floor. (He is not an exercise nut.)

I read this riddle before. Will not spill the beans now.

It took me a while, but I think I remember this from long ago. I never would have come up with the answer on my own, it's a bit contrived IMO (there are workarounds). But clever, entertaining.

white text spoiler alert:

edit/add: reminded me of this thread (had to cut the htttp stuff or it showed up in blue) : .... am-i-crazy-for-wanting-cosmetic-surgery-111983 ....

-ERD50

 

[kgtest]

My favorite (and I wish I had a copy of it) was a simple series of additions and subtractions on a strip of paper. As each operation was completed, the paper was rolled to the next operation that used the result from the previous operation. Seriously, there were no tricks within the operations. I never saw anyone in my Jr. Hi class get it right - including two math teachers.

It turned out to be one of those crazy things where your mind leaps ahead (perhaps making you end up with 4000 instead of 3100 or perhaps 3900. I forget just how it worked but I never saw it fail. - even when everyone had heard about it.) YMMV

My mom showed me a similar math problem a month or so ago. I got a kick out of it.

 

[NW-Bound]

I stumbled upon this simple looking math problem last week and showed it to several people and have not found anyone that got it right, including my daughters 6th grade math teacher. It took Albert Einstein an hour to figure it out.

If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?

I don't believe that Einstein took 1 hour to figure this out. Many posters, myself included, took a second or two.

The above puzzle would be similar to this one I just thought of.

A member of this forum was able to save an amount that allowed him to retire early at the age of 40, using a WR of 4% of the initial stash (à la Trinity study). He was truly convinced that this WR was safe for his planned retirement period of 50 years, and would not reduce his WR no matter what the market did.

It so happened that in the 1st half of his retirement, the market return was flat, and barely caught up with inflation.

Now, the question: What is the minimum market return he would need for the 2nd half of his retirement?

 

[RockLife]

I stumbled upon this simple looking math problem last week and showed it to several people and have not found anyone that got it right, including my daughters 6th grade math teacher. It took Albert Einstein an hour to figure it out.

If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?

To average 60mph (a mile a minute) over 2 miles, it will take 2 minutes. Now, you just averaged 30mph over the first mile, which takes 2 minutes. So for the second mile you have to go slightly faster than the speed of light and you'll still be late!

 

[Car-Guy]

To average 60mph (a mile a minute) over 2 miles, it will take 2 minutes. Now, you just averaged 30mph over the first mile, which takes 2 minutes. So for the second mile you have to go slightly faster than the speed of light and you'll still be late!

Sounds like it might be easier to calculate the absolute value of Pi.

 

[ERD50]

....
The above puzzle would be similar to this one I just thought of.

A member of this forum was able to save an amount that allowed him to retire early at the age of 40, using a WR of 4% of the initial stash (à la Trinity study). He was truly convinced that this WR was safe for his planned retirement period of 50 years, and would not reduce his WR no matter what the market did.

It so happened that in the 1st half of his retirement, the market return was flat, and barely caught up with inflation.

Now, the question: What is the minimum market return he would need for the 2nd half of his retirement?

I don't think this is as simple as you might be thinking? I think it depends on the inflation rate, and what you mean by "barely keeping up with inflation".

If the portfolio keeps up with inflation, then the gains are on the entire portfolio vs an inflation adjustment on the smaller W/D amount. In that case, high inflation would be a good thing for the retiree.

EX: Starting $1,000K portfolio, starting $40K W/D at the start of the year. 10% inflation for easy math.

Portfolio is $960K on Jan 2, then gains 10% over the year, to $1,056K at EOY. But the 10% increase for the WD brings it to $44K, and Jan 2 of year 2 portfolio is higher than start, 1056-44 = $1,012K.

Repeat with 1% and the portfolio drops.

I'm assuming you were thinking in terms of no inflation and no gain. In that case, the 4% depletes the portfolio in 25 years, and just like the OP problem, there is no way to make it up in the last half.

-ERD50

 

[NW-Bound]

I don't think this is as simple as you might be thinking? I think it depends on the inflation rate, and what you mean by "barely keeping up with inflation".

If the portfolio keeps up with inflation, then the gains are on the entire portfolio vs an inflation adjustment on the smaller W/D amount. In that case, high inflation would be a good thing for the retiree.

EX: Starting $1,000K portfolio, starting $40K W/D at the start of the year. 10% inflation for easy math.

Portfolio is $960K on Jan 2, then gains 10% over the year, to $1,056K at EOY. But the 10% increase for the WD brings it to $44K, and Jan 2 of year 2 portfolio is higher than start, 1056-44 = $1,012K.

Repeat with 1% and the portfolio drops.

I'm assuming you were thinking in terms of no inflation and no gain. In that case, the 4% depletes the portfolio in 25 years, and just like the OP problem, there is no way to make it up in the last half.

-ERD50

Your calculation showed the artifact of lump sump withdrawals.

If the retiree withdrew $40K on Jan 1st, and tried to live on it for the whole year with a rampant 10% inflation, he would find himself running short towards the end of the year, and would have to make supplemental withdrawals. He would have to. In December, his dollars had only a bit more than 90% of the purchasing power they had in January.

If our guy took money out as he needed it, his withdrawals would go up continuously throughout the year at the same rate as inflation and the growth of his hypothetical stash. Then, in "constant purchasing power dollars", a return matching inflation exactly would be the same as no inflation and no return.

PS. In real life, a return matching inflation is worse than no inflation/no return. It's because you may have to pay taxes on the "phony" investment returns that do not give you more purchasing power. You lose.

 

[Archman]

90 mph Just basic algebra.

ave = (x + y)/2
60 = (30 +y)/2
120 = 30 + y
120-30 = y
90= y

You haven't read much of this thread, have you?

As I mentioned upstream, https://www.early-retirement.org/fo...-that-stumps-everyone-113785.html#post2764408

"This thread is a great example of "Thinking, Fast and Slow".

Your algebra itself is fine (fast thinking), but it doesn't apply to the problem in the OP (requires a bit of slow thinking). So your answer, based on basic algebra, is very wrong.

-ERD50

The original post doesn't give any conditions that would invalidate my answer. Many algebraic story problems in text books aren't realistic.