Puzzles

[Kermit1941]

Sally made three cubes out of modeling clay. The smallest of the three was 3 centimeters by 3 centimeters by 3 centimeters. The next largest was 4 centimeters by 4 centimeters by 4 centimeters. The largest was 5 centimeters by 5 centimeters by 5 centimeters. The cubes are all full cubes, not just edges strung together. Sally smashed the three cubes into one solid lump, and then made a larger single cube from them. How many centimeters is the edge of this new single cube?

[Thad]

6 cm

More?

[Hotspring 44]

I think, 8 cm cube.

I am not into math that much so I could be wrong, but here is what I came up with:

(3x3x3)+(4x4x4)+(5x5x5)=216
(27) + (64) + (125) =(216)÷(27)=8
(27 one cm cubes)+ (64 one cm cubes)+ (125 one cm cubes)= (216 one cm cubes) ÷ (3cubed)=8 Note: 3 cubed = 27.

[Hotspring 44]

Oops!!... ...I was Wrong; Thad got it correctly.
It is 6 not 8 because:
The cube root of 216 is 6
because 6^3 = 6*6*6 = 216. (Whatever that means LOL!).

I found that by going to: Ask Dr Math.
.

I think, 8 cm cube.

[Kermit1941]

6 cm

More?

Second puzzle:

A box is 3 inches high, 4 inches from front to back,
and one foot, from left side to right side.

What is the distance from the
lower front left corner to the
upper back right corner?

Kermit

[Thad]

13 inches

visualizing a plane between left corner bottom and the two points of the diagonal of a 3x4 rectangle on the right and a2+b2 = c2 solves for both

[Kermit1941]

On a cold, windy day, ten year old Daniel went on a short walk with his father and two uncles. All four wore hats. Only Daniel's hat was tied on. A sudden gust of wind blew off the hats of the three adults. Daniel retrieved the hats, but did not notice the differences among them. He gave the hats back ran...domly. What is the probability that exactly two of the men got their own hat back?

[Kermit1941]

Three models walk down the show off lane to the audience. They are named,
Miss Blue, Miss Pink, Miss Green. Each wears a dress of solid color. Miss Blue remarks,
"We are each wearing a dress of solid color, Green, Pink, or Blue, yet, none of us is wearing a color that matches our name.
The lady wearing green comments,... "That's quite a coincidence."
What color dress is each lady wearing?

[Kermit1941]

Show how to calculate, in less than a minute, the difference between; the sum of all the odd positive integers less than a million, and the sum of all the even positive integers less than a million.

[Kermit1941]

A third of the students in the math class are girls. On the final exam, the girl's average score exceeds the class average by 6 points. The boy's average score is how many points below the class average?

[Kermit1941]

Numbers one through six line up for inspection. They do not line up in numerical order.

The fourth number in line is the difference of the first two numbers in line. The fifth number in line is the difference of the second and third number in line. The last number in line is the difference of... the two numbers ahead of em.

What are the eight possible ways that the six numbers are lined up?

[Kermit1941]

In his 'Last will and testament', the father did "bequeath to my beloved only daughter 1/4 of my fortune, 1/3 of what remains to my younger clever son, and 1/2 of what remains to my ambitious elder son, and the rest to my always beautiful wife".

Who had the greater share?

[Hotspring 44]

They each are wearing (coincidentally) a mismatched color.

Three models walk down the show off lane to the audience. They are named,
Miss Blue, Miss Pink, Miss Green. Each wears a dress of solid color. Miss Blue remarks,
"We are each wearing a dress of solid color, Green, Pink, or Blue, yet, none of us is wearing a color that matches our name.
The lady wearing green comments,... "That's quite a coincidence."
What color dress is each lady wearing?

[Thad]

it has be zero probability that exactly two got their hats back because that would mean they all got their hats back, can you show the math for this if that is wrong.

On a cold, windy day, ten year old Daniel went on a short walk with his father and two uncles. All four wore hats. Only Daniel's hat was tied on. A sudden gust of wind blew off the hats of the three adults. Daniel retrieved the hats, but did not notice the differences among them. He gave the hats back ran...domly. What is the probability that exactly two of the men got their own hat back?

[Thad]

they all got equal shares

In his 'Last will and testament', the father did "bequeath to my beloved only daughter 1/4 of my fortune, 1/3 of what remains to my younger clever son, and 1/2 of what remains to my ambitious elder son, and the rest to my always beautiful wife".

Who had the greater share?

[Hotspring 44]

The father did.... ...The father "had" the greater share.

In his 'Last will and testament', the father did "bequeath to my beloved only daughter 1/4 of my fortune, 1/3 of what remains to my younger clever son, and 1/2 of what remains to my ambitious elder son, and the rest to my always beautiful wife".

Who had the greater share?

[Hotspring 44]

Purely a guess off the top of my head [pun]; 1 in 9.

On a cold, windy day, ten year old Daniel went on a short walk with his father and two uncles. All four wore hats. Only Daniel's hat was tied on. A sudden gust of wind blew off the hats of the three adults. Daniel retrieved the hats, but did not notice the differences among them. He gave the hats back ran...domly. What is the probability that exactly two of the men got their own hat back?

[Thad]

Kermit

I have to admit my embarrassment at having high school algebra be such a challenge, I don't it use it much in what I do.

I wish I had been led to math in such a way that I would now be able to write fluently in calculus, alas it is not to be but rather than reinvent the wheel perhaps you might supply a sentence.

I wish you would show a mathematical formula that might be a very useful thing to have for an argument I believe to be important.

Your background in programming for economics is perfect.

How would you write a formula and proof showing the progression of decline in burden and cost of the
economics of one person up to 27 people, exponentially.

the principle based on two can live cheaper than one and then how much 3 can live cheaper than 2 etc. up to 27

including things like the cost and time of someone cooking dinner who does not cook nor enjoy it compared to that same person opting to eat out, or having one of the group who enjoys doing that but not the building or the sewing or the driving or the etc. and the cost comparison in time saved, and aggravation avoided etc. in all the base functions including social life of going out for enjoyment compared to enjoying ones fellows more at home.

At this phase its seems designing the question is still in progress but since you charge for mathematical help how would you estimate this request for a final price?
The point of doing this publicly is that it is part of a thread that has been idled for want of this formula.

[Kermit1941]

Kermit

I have to admit my embarrassment at having high school algebra be such a challenge, I don't it use it much in what I do.

I wish I had been led to math in such a way that I would now be able to write fluently in calculus, alas it is not to be but rather than reinvent the wheel perhaps you might supply a sentence.

:) It will take less work than you imagine to become fluent in calculus.

I wish you would show a mathematical formula that might be a very useful thing to have for an argument I believe to be important.

Your background in programming for economics is perfect.

How would you write a formula and proof showing the progression of decline in burden and cost of the
economics of one person up to 27 people, exponentially.

This is actually a quite complicated topic.

We can't do justice to it in any one discussion.

The attached file shows the work that one team of economists
did to attack this problem.

You might find it useful to look in this paper, not at the
mathematical part, but in the non-mathematical part,
where they discuss what household factors they considered, and why.

Seek to understand the simplifying assumptions they made in order to
treat the topic mathematically.

Are any of the simplifying assumptions so far off the mark as to render
the mathematical formulas into non-sense?

the principle based on two can live cheaper than one and then how much 3 can live cheaper than 2 etc. up to 27

Why 27?

including things like the cost and time of someone cooking dinner who does not cook nor enjoy it compared to that same person opting to eat out, or having one of the group who enjoys doing that but not the building or the sewing or the driving or the etc. and the cost comparison in time saved, and aggravation avoided etc. in all the base functions including social life of going out for enjoyment compared to enjoying ones fellows more at home.

As you browse the attached PDF, you might find additional factors to consider.

At this phase its seems designing the question is still in progress

Yes. And researching it might lead to other economic terms,
such as "comparative advantage", "Division of labor", "Specialization",
"Household economy of scale".

but since you charge for mathematical help how would you estimate this request for a final price?
The point of doing this publicly is that it is part of a thread that has been idled for want of this formula.

I'm not really qualified to easily answer this question or lead the
discussion of it.


I'm willing to participate in the discussion of it, for my own information.

I don't promise to provide any answers, nor would I charge for
any useful contributions I happen to make.

Kermit Rose

[hales]

"0" I think that if one man got the right hat then the other two would not have the right hats, otherwise, I think it would be true that either all three, or none of the men had the right hat.. ; )

On a cold, windy day, ten year old Daniel went on a short walk with his father and two uncles. All four wore hats. Only Daniel's hat was tied on. A sudden gust of wind blew off the hats of the three adults. Daniel retrieved the hats, but did not notice the differences among them. He gave the hats back ran...domly. What is the probability that exactly two of the men got their own hat back?