Mathematics Brain Teasers.

[danydandan]

7 hours ago, Habitat said:

Whatever the nett worth of the world's richest man is. Plus a little more. Let's be very generous, and say $200 Billion

1.26 or something like that. Can't get exactly 200 billion without add numbers after the decimal point.

[Habitat]

5 minutes ago, danydandan said:

1.26 or something like that. Can't get exactly 200 billion without add numbers after the decimal point.

I thought it was less, but let's not quibble, it is a tiny, tiny amount. Moral of the story, interest on funds has a countervailing risk of losing the principal, that will kick in eventually. Totally "safe" compound interest is impossible.

[danydandan]

37 minutes ago, Habitat said:

I thought it was less, but let's not quibble, it is a tiny, tiny amount. Moral of the story, interest on funds has a countervailing risk of losing the principal, that will kick in eventually. Totally "safe" compound interest is impossible.

Actually it is less, a lot less. That's what happens when you do stuff in your head. It's less than a cent. Isn't it?

I worked it back from 200,000,000,000,000,000. Not 200,000,000,000. Too many bloody zeros. Why you doing this to me this early in the morning Hab? The actual answer is like 0.000001

Thanks for that Habitat. Made my head explode at 6am. Lol. 

Edited October 31, 2018 by danydandan

[danydandan]

A pontoon has vertical sides, a regtangular base 20m long and 4m wide. The ends slope at 45degree to the horizontal. If it floats in water with it's base 16cm below the surface. What is it's mass? 

Archimedes will be proud of us for including this!

Edited October 31, 2018 by danydandan

[Ozymandias]

Depends on whether the pontoon floats in fresh water or sea water. In any case, ...

Weight of the Pontoon (W) = Buoyancy Force (F)  [Newton's Third Law]

pontoon mass x grav.acc.  =  mass of water displaced  x  grav.acc.

                   pontoon mass = mass of Displaced Water 

                                           = Vol. Water Displaced (m^3) x  Density Water (rho)

                                           = 2{4[(10 x 0.16) + 0.5(0.16)(0.16)]} x 1000kg/m^3

                                           = 12.9024m^3 x 1000kg/m^3   (fresh water) 

                                           = 12,902.4kg  =  12.9 tonne

or                                        = 12.9024m^3 x 1025kg/m^3   (sea water)

                                           = 13,225kg  =  13.225 tonne

Sorry for the solution. In my view, an outline solution and method should always be given.

Edited October 31, 2018 by Ozymandias

[danydandan]

1 hour ago, Ozymandias said:

Depends on whether the pontoon floats in fresh water or sea water. In any case, ...

Weight of the Pontoon (W) = Buoyancy Force (F)  [Newton's Third Law]

pontoon mass x grav.acc.  =  mass of water displaced  x  grav.acc.

                   pontoon mass = mass of Displaced Water 

                                           = Vol. Water Displaced (m^3) x  Density Water (rho)

                                           = 2{4[(10 x 0.16) + 0.5(0.16)(0.16)]} x 1000kg/m^3

                                           = 12.9024m^3 x 1000kg/m^3   (fresh water) 

                                           = 12,902.4kg  =  12.9 tonne

or                                        = 12.9024m^3 x 1025kg/m^3   (sea water)

                                           = 13,225kg  =  13.225 tonne

Sorry for the solution. In my view, an outline solution and method should always be given.

Yeap. Your turn. Hopefully @Habitat will continue to participate.

[Ozymandias]

3 hours ago, danydandan said:

Yeap. Your turn. Hopefully @Habitat will continue to participate.

Maybe I shouldn't have answered so quickly? I'll set a question (but I'll stay off the thread for a while to let others have a go and find their feet):

This is a rather famous/infamous problem whose solution relies on PERSPECTIVE, or how you LOOK at it, and does not require any maths other than that used in counting (natural numbers):

16     06     68     88     X     98 

What is X?

[danydandan]

20 hours ago, Ozymandias said:

Maybe I shouldn't have answered so quickly? I'll set a question (but I'll stay off the thread for a while to let others have a go and find their feet):

This is a rather famous/infamous problem whose solution relies on PERSPECTIVE, or how you LOOK at it, and does not require any maths other than that used in counting (natural numbers):

16     06     68     88     X     98 

What is X?

People's this is relly easy. 

However there actually is a pattern. 1,2,1,2,1,2........ Etcetca. 

X can also be anything. But the most logical answer for X is L8. Yes L8. 

[Ozymandias]

6 hours ago, danydandan said:

People's this is relly easy. 

However there actually is a pattern. 1,2,1,2,1,2........ Etcetca. 

X can also be anything. But the most logical answer for X is L8. Yes L8. 

I can't agree, Dan, although I know some people make that arguement. The answer is 87. The row or sequence presented in the problem is merely viewed upside-down:

16    06    68    88    X     98

If you view it correctly from above you will see

86    X    88     89    90    91

The missing number is 87 not an upside-down L8.

But you should set the next teaser.

[danydandan]

23 minutes ago, Ozymandias said:

I can't agree, Dan, although I know some people make that arguement. The answer is 87. The row or sequence presented in the problem is merely viewed upside-down:

16    06    68    88    X     98

If you view it correctly from above you will see

86    X    88     89    90    91

The missing number is 87 not an upside-down L8.

But you should set the next teaser.

That's true. 

I'll try think one up tomorrow.

[danydandan]

0.999=1 

True or false?

Why?

[Ozymandias]

'Is there anybody there?', said the Traveller,

Knocking on the moonlit door,

As his horse in the silence champed the grasses

Of the forest's ferny floor.

[+joc]

On 11/2/2018 at 1:43 PM, danydandan said:

0.999=1 

True or false?

Why?

False...

...because 1 oz of pure water will not kill you...but .998 oz of pure water + .001 oz Ricin will. 

[Ozymandias]

4 hours ago, joc said:

False...

...because 1 oz of pure water will not kill you...but .998 oz of pure water + .001 oz Ricin will. 

I agree, joc. 0.999 does not equal 1, but not for the reasons you cite.

0.999 only equals 999 thousandths of unity. It is short by one thousandth.

However, 0.999..., with 9 repeated to infinity, does equal 1 and their are many proofs of that.

Edited November 4, 2018 by Ozymandias

[danydandan]

It's an argument either way.

Taking the numbers literally it's obviously an false statement. However using the law of infinity it's actually a true statement. 

Either answer is acceptable! The why is more important than the actual result in this case. 

@joc you answered first so you can set the next question.

[Ozymandias]

8 minutes ago, danydandan said:

It's an argument either way.

Taking the numbers literally it's obviously an false statement. However using the law of infinity it's actually a true statement. 

Either answer is acceptable! The why is more important than the actual result in this case. 

@joc you answered first so you can set the next question.

You cannot invoke the sum to infinity here since you didn't present 0.999 as a non-terminating decimal number.

[+joc]

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later.
What time is it now?

[danydandan]

31 minutes ago, Ozymandias said:

You cannot invoke the sum to infinity here since you didn't present 0.999 as a non-terminating decimal number.

Don't have to really, there are multiple proofs like. Geometric Series, Algebraic Arguments, Semantics, Precedent Arguments (other pre-calculus ones) and some very weak philosophical arguments. 

That's why I chose the question, there is basically no wrong answer. Also hoping it would result in some nice conversation.

[Ozymandias]

24 minutes ago, danydandan said:

Don't have to really, there are multiple proofs like. Geometric Series, Algebraic Arguments, Semantics, Precedent Arguments (other pre-calculus ones) and some very weak philosophical arguments.

Dan, in fairness and as a matter of principle, nobody can prove that 0.999 is equal to 1 because it simply is not. 

The mathematical arguments you cite are for proving that the repeating, non-terminating, decimal number 0.999 .... is equal to 1.

[danydandan]

48 minutes ago, Ozymandias said:

Dan, in fairness and as a matter of principle, nobody can prove that 0.999 is equal to 1 because it simply is not. 

The mathematical arguments you cite are for proving that the repeating, non-terminating, decimal number 0.999 .... is equal to 1.

I did assume that people would know .999 was equal to .9999..... I guess I shouldn't have.

I take your point.

@joc 21:00 is the answer to your riddle.

Edit: No 21:30. 

Edited edit: No was right the first time. 21:00

Edited November 4, 2018 by danydandan

[danydandan]

Well @Ozymandias I have officially got a month out of this thread. Happy days!

[Ozymandias]

52 minutes ago, danydandan said:

Well @Ozymandias I have officially got a month out of this thread. Happy days!

I love the thread! I only wish more people would get involved. There are plenty of contributors to other science oriented threads who could show an interest here. I'm more than happy to keep contributing if you - and others -  are.

[Ozymandias]

Dan, it's your turn again to set a teaser/problem.

[danydandan]

Just now, Ozymandias said:

Dan, it's your turn again to set a teaser/problem.

I'm gonna leave it open for someone else to set one. 

If no one else has put one forward I'll stick one up tomorrow. I'll try make as easy as I can.

[danydandan]

It was Debbie's first day at school. The teacher suggested that it would be a good idea for each child to meet every other child in the class. The teacher said, "When you meet, please shake hands and introduce yourself by name."

If there were 15 children in the class, how many total handshakes were there?