The Mathematics Thread

[moa999]

I won't give it away, but the answer is very simple if you can see it.

Agreed.
I would like to see someone do it the long way though

 

[TheRealTMA]

Agreed.
I would like to see someone do it the long way though

Why? It's really just a trivial problem with misdirection.

 

[david1]

Why? It's really just a trivial problem with misdirection.

Because where's the fun in taking shortcuts all the time

 

[anat0l]

Here's another good one if you haven't seen it before: Two trains, 100 miles apart, are approaching each other on the same track, one going 30 miles per hour, the other going 20 miles per hour. A bird flying 120 miles per hour starts at train A (when they are 100 miles apart), flies to train B, turns around and flies back to the approaching train A, and so forth, until the two trains collide. How far has the bird flown when the collision occurs?

Got an answer - seems deceptively simple; no idea if mine is the long or short way.

I guess you could do it by plotting the paths of the three objects on a Cartesian plane. Seems like an odd way to do it, though, once you get nearer to the time of collision, unless there is some sum of series which I'm missing.


Here's another deceptively simple question. It appears in all sorts of various forms, and apparently is a paradox.

A large container of soaked sponges weighs 50 lb[sub]m[/sub] and is 99% water. After being left in the open overnight, it is found the next day that some of the water has evaporated such that the contents are now 98% water. How much does the contents of the container now weigh?

 

[incumbent]

Got an answer - seems deceptively simple; no idea if mine is the long or short way.

I would imagine the long way focuses on the path flown, the short way on the time flown.

 

[russ]

Calculating the number of miles is easy
The hard part is working out how many status credits it gets and whether it gets lounge access on either train

 

[TheRealTMA]

Calculating the number of miles is easy
The hard part is working out how many status credits it gets and whether it gets lounge access on either train

Perhaps you get one for each touch of the bird? That makes the problem more interesting!

 

[TheRealTMA]

A large container of soaked sponges weighs 50 lb[SUB]m[/SUB] and is 99% water. After being left in the open overnight, it is found the next day that some of the water has evaporated such that the contents are now 98% water. How much does the contents of the container now weigh?

Impossible to answer without knowing the time dependent adsorption coefficient of hydration of the potatoes.

 

[whatmeworry]

Multiplying with lines.

[video=youtube;_AJvshZmYPs]https://www.youtube.com/watch?v=_AJvshZmYPs[/video]

 

[RooFlyer]

Could you find the cubed root of 32461759 by 'long working out' on paper?

In some research for a book I'm doing, I've found a c.1830s notebook of a farming pioneer that gives the 'rules to extract a cubed root'. Fascinating stuff. I'll post workings a bit later.

 

[moa999]

Ends in a 9.
300 cubed is 27000000
400 cubed is 64000000 so closer to 300

My first guess was then correct

But more logical guesswork.
An actual method would be interesting.

 

[RooFlyer]

So here are some of the notebook pages. The explanation first, then two worked examples. The main part of the book is taken up by this 1830s farmer's accounts.

 

[anat0l]

So here are some of the notebook pages. The explanation first, then two worked examples. The main part of the book is taken up by this 1830s farmer's accounts.

...

It doesn't apply in this case, but if the cube root is between 1 and 100 (i.e. if the number to find the cube root of is 1,000,000 or less), there is an extremely concise way to find the cube root.


Here's a problem which apparently went viral and comes thanks to Google.

Using the numbers 1 1 5 and 8, make the number 10. The rules were:

• You can use + - * / ( )
• Each number must be used exactly once. You can't omit using any of the numbers.
• No decimal points, no factorials, no square roots, no exponents, no combining the numbers together to form new numbers (e.g. you can't take the two 1s and make the new number 11).

There is only one solution.

 

[anat0l]

Oldie but a goodie... and it's better than that R DR R stuff from The Simpsons:

 

[whatmeworry]

Try this on your friends.

First ask your friend to think of their shoe size, then – using a calculator or a pen and paper – they should multiply it by five.
Next they add 50, and then take that total and multiply it by 20. They should add 1,015, and finally subtract the year of their birth.
Magically, the result should be their shoe size and age, together making up a three or four-digit number. The trick works regardless of whether you use UK, European or American shoe measurements.
However, it won’t work for someone who has already had their birthday this year, or who is more than 100 years old.

​

 

[TheRealTMA]

Try this on your friends.

Just a slight of hand trick.

 

[rainbowgirl]

Try this on your friends.

Creepy. When I saw the 1015 I could see how the age was going to end up in the final figure but the rest is just weird.

 

[anat0l]

Creepy. When I saw the 1015 I could see how the age was going to end up in the final figure but the rest is just weird.

Try this on your friends.

Kind of easy to prove, actually.

Let your shoe size be s. If you follow all the steps up to subtracting the year of your birth, you will get 100s + 2015.

2015 - y, where y is the year of your birth, gives you your age in years at the end of 2015, i.e. how old you turned last year. This is why it doesn't work if you've already had your birthday this year (2016).

100s simply takes the shoe size and places the last digit of it in the "hundreds" place. This is why it works regardless of whether your shoe size is 1, 2 or even 3 digits long. This is also why it doesn't work if you are aged over 100. It also doesn't work nicely if your shoe size has a fraction in it; for example, if you were born in 1980 (age 35 last year) and have a shoe size of 9.5, you will get a final result of 985.

 

[medhead]

Re: How to get the blood pumping...

I have a mathematics/logic problem for you all. This is actually a real world problem that is current for me. Yes, I understand this is the playground. But I just don't see the point in starting a new thread to help me solve my maths problems - Therefore this thread seems appropriate.

I have $209 remaining on a UATP card. This card can be used to pay for Qantas flights only. The flights do not earn points/SC. To use online the value of the airfare has to be lower than the balance on the UATP card. Within the valid period of the UATP card I need to buy airfares of $181, $376 and $125.

I wish to minimise the wasted remaining balance on the UATP card. I assume calling to make a mixed payment will result in a phone assistance fee of $35. The only method of multiple online payments that seems possible is to use a gift vouchers ($50, $100, $150 etc.) and then pay the balance with the UATP.

Is there a combination of gift vouchers that can be used with the card to leave less than $35 remaining balance?

 

[russ]

Re: How to get the blood pumping...

https://en.wikipedia.org/wiki/Linear_programming