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abcxyz
Posted: Saturday, March 12, 2011 10:25:48 PM
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Etcheparre wrote:
This isn't really a problem, more of a magic trick. Here's how the trick works:
The "magician" asks someone to write a random four digit number on a sheet of paper, anything between 0001 and 9999. Then the "magician" writes a number on another sheet of paper and hides it; he then asks the same person to write another four digit number under the other number. The magician then writes a four digit number under the two other numbers, the "victim" writes another four digit number and the magician then writes another number. The sum of all these numbers is equal to the number he wrote on the other sheet of paper.

For instance:
7898 the magician writes 27898 on the other sheet, shows it to no one
2546
6556 written by the magician
4789
6109 written by the magician
Sum of all five is equal to 27898

I understand how he does it mathematically, what surprises me is how quickly he does it. I've devised a means to make it work but it involves some basic calculus, while this trick was shown to me by a drunken bartender, which most probably didn't do much calculus...

Anyone have a smart method for this?



Etcheparre, no calculus here. You notice for 7898 the magician writes 27898, which means he will have to make the sum of the next 4 numbers 20000. The sum of the first two numbers 2546 and 6556 are 9102 and the sum of the next two is 10898. For the magician, the sure-shot way to make the sum 20000 would be: after the 'victim' has written the first of the 4 numbers, 2546 in this case, write 10000-2546 as your second number. For your 4th number, write 10000- the third number. That way you get your desired sum.
1.2546
2.6556 written by the magician....... first sum=9102
3.4789
4.6109 written by the magician... second sum=10898
first sum+second sum=20000

But after thinking a while your victim will eventually figure out your trick. So to make it a bit complex you target to make the first sum a number over 9000 but less than 10000, or over 10000 and close to 11000 but not 11000, depending whether the first number is over 9000. For example, you want to make the two sums 9314 and 10686. The trick will go like
9284 - you write 29284
8624
2062 - you (subtracting 8624 from 10686)
5928
3386 - you (subtracting 5928 from 9314)

You have to be flexible about what you want the two sums to be during the trick and you should decide on what you want the sums to be after the first number is written, but you must keep the 2 sums within 9000 and 11000. Remember, this method is not foolproof. But usually your victim will not use the same digit (especially 9 and 1) twice as the first digit of the two numbers he will write, and in his desire to be random, he will pick the numbers he has not used yet, so choose your set of sums after you have seen his first number (first two numbers actually, if you consider the one written initially).
Your bartender would not have got his show if the third number (4789) were greater than 9898. Then he wouldn't have had any 4 digit number that could make the sum 20000. Looks like he was a bit daring with this trick. So now that you know the trick, if you want to get even with him, ask him to show you the trick again and this time instead of 2546 and 4789, choose both the numbers as 9999.
Etcheparre
Posted: Monday, March 14, 2011 5:27:34 AM
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Yeah that's what I basically gathered after thinking about it a bit; you "control" two numbers, the other person "controls" two other numbers, so you're free to have their sum be 20000.

My "error" came from the fact that I actually cared what the first number was, meaning that I basically had to do an addition and a subtraction at the same time. For instance if the first number was 2546, I'd write 22546 on my sheet of paper, he'd then write his second number, 7898, and I'd calculate 12000-(2546+7898)=X, with X being my first number. All I had to do was 10000-7898=X...

But as you said, if he isn't careful, he can easily be trapped :p

Thanks!
abcxyz
Posted: Tuesday, March 15, 2011 1:04:15 AM
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you're welcome :)
ppv117
Posted: Wednesday, March 26, 2014 6:26:51 AM
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A long multiplication exercise...

(x-a)*(x-b)*(x-c)........*(x-z)

Answer = ?

4 Options.......

1. answer starts with x^26
2. answer starts with x^25
3. zero
4. infinity

Anyone ?
ppv117
Posted: Wednesday, March 26, 2014 10:13:53 AM
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I am presenting one more puzzle....

1 Rupee = 100 paise (Indian currency)
= 10 * 10

Now 10 paise is equal to 0.10 Rupee

= 0.1 * 0.1
= 0.01

And 0.01 Rupee is = 1 paise !!!

What happened ?

Anyone with answer ?
Audiendus
Posted: Wednesday, March 26, 2014 7:47:10 PM
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ppv117 wrote:
A long multiplication exercise...

(x-a)*(x-b)*(x-c)........*(x-z)

Answer = ?

4 Options.......

1. answer starts with x^26
2. answer starts with x^25
3. zero
4. infinity

Zero, because one of the numbers to be multiplied is (x-x), which equals zero.


I don't understand your second puzzle.
0.10 Rupee = 0.1 * 0.1 ???
Shivanand
Posted: Wednesday, March 26, 2014 11:52:51 PM
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Hi ppv, fractions cannot be multiplied the way you have done! 10 time 10 is hundred but 0.1 time 0.1 is 0.01!


Cheers!
ppv117
Posted: Thursday, March 27, 2014 10:10:17 AM
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Let me re-write my second puzzle.

1 rupee = 100 paise
= 10 * 10
= 0.1 * 0.1 (10/100 = 0.1 rupee)
= 0.01
= 1 paise !

I am sure it is now clear.
Audiendus
Posted: Thursday, March 27, 2014 10:43:19 AM
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ppv117 wrote:
1 rupee = 100 paise
= 10 * 10
= 0.1 * 0.1 (10/100 = 0.1 rupee)
= 0.01
= 1 paise !


Ah, I get it! The flaw in the reasoning is as follows:

1 rupee = 10 paise * 10 (not 10 paise * 10 paise – that would be 100 "square" paise!).
So you cannot replace the blue "10" with the blue "0.1".

1 rupee = 10 paise * 10 = 0.1 rupee * 10 = 100 paise.
ppv117
Posted: Friday, March 28, 2014 9:49:30 AM
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You are right, Audiendus.

ppv117
Posted: Friday, March 28, 2014 9:56:59 AM
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This is not a puzzle, but I do hope math and science related questions can be accommodated. If I am stepping out of line, please do mention here ........so I would know...

If a refrigerator is left open (door open) in a closed room ...,

Will the room temperature,

A. Increase

B. Decrease

C. Such a condition cannot have any effect at all on room temperature.

IMcRout
Posted: Friday, March 28, 2014 12:41:36 PM
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If it is NOT switched on, nothing will change.
If it is NOT switched on, but had been working until shortly before opening, the room temperature will sink for a very short while and then return to what it was before.
If it IS switched on, the temperature will sink for a very, very short time and then rise, because the fridge keeps working and working and working and will thus get very, very warm.
ppv117
Posted: Saturday, March 29, 2014 9:38:40 AM
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I am sorry, IMcRout, if I allowed confusion to creep in.

I meant the refrigerator to be switched on and working at full capacity.

You may further take that the room was all normal...and then a non-working frig is brought in....then switched on with its door(s) open, and then room is sealed thermally.

I do hope I have clarified sufficiently.
ppv117
Posted: Saturday, March 29, 2014 9:40:53 AM
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I am very happy to be part of this forum. Let's make it more exciting with many entries and puzzles and so on.
Drag0nspeaker
Posted: Saturday, March 29, 2014 12:21:50 PM

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Hello ppv!

In a perfect world . . . Boo hoo!

If the fridge were perfectly efficient, as a heat-pump, it would remove heat from the 'inside of the fridge' and pump the same heat out of the back coils. These amounts of heat would be the same, so the amount of energy in the room would remain the same.

Practically, the fridge motor will produce heat, so the room will become warmer.

ppv117
Posted: Monday, March 31, 2014 10:08:52 AM
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Hey Dragon....you are absolutely right.

Room temp will rise because of inefficiency of the system.

I will come up with something. Let's keep this forum alive.
ppv117
Posted: Monday, March 31, 2014 10:20:42 AM
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We need a screen to be able to see anything. Light falls on objects and rebounds and reaches our eyes......which fact then makes objects visible.

On what screen is a rainbow seen ? Obvious answer comes to mind is ..water droplets in sky. But if light is passing through droplets to reach our eyes........how then droplets are still the screen on which we see a rainbow.

Basically a simple problem.....writing only to keep things alive...
Audiendus
Posted: Tuesday, April 1, 2014 7:46:17 AM
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ppv117 wrote:
We need a screen to be able to see anything. Light falls on objects and rebounds and reaches our eyes......which fact then makes objects visible.

Not all light we see has been reflected. Some light reaches us directly, e.g. from the sun and stars.

I suppose that some reflection of light would be necessary for us to see the water droplets as objects. But as the droplets merely serve to split up the sunlight into unobjectified patches of colour, I don't think reflection is necessary.

That is my guess, anyway. Think
Drag0nspeaker
Posted: Tuesday, April 1, 2014 6:15:41 PM

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The "screen" is the back surface of the water droplets.



[image not available]


A bit like those super-reflective cinema-screens made up of millions of little glass balls . . .

**************
If the speed of light is a constant, how can the blue light (which travels further) go through the ball in the same time as the red light?
ppv117
Posted: Wednesday, April 2, 2014 3:04:15 AM
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Absolutely correct.

The sunray undergoes internal reflection (from back surface) and then refraction to give us a rainbow.

ppv117
Posted: Thursday, April 3, 2014 11:45:03 AM
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A bicycle is fitted with a fork on the front wheel. It connects the governing / steering handles to the centre of the front wheel.

Why is this fork never perfectly straight. It is typically straight in the upper part and then curving slightly before it meets the front wheel centre.
Shivanand
Posted: Friday, April 4, 2014 12:04:36 AM
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I guess it is because the road induced shock gets applied radially and not transmitted to the handle bar directly! Also, there would be bit of torsional spring action, reducing the shock.d'oh!
ppv117
Posted: Friday, April 4, 2014 6:15:40 AM
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Many bicycles have separate spring shock absorbers.

It is about steering. Draw a straight line from the centre of the steering handle through the fork. For good steering, this straight line should end where the front wheel is in point contact with the ground.

If the fork were straight, the straight line would not end at the wheel-ground contact point.

I am unable to attach a sketch to elaborate but if you search the web with some specific key-words, detailed explanation is surely somewhere on the web.
Barely literate
Posted: Wednesday, April 9, 2014 5:09:51 PM

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Hi ppv,

The very you is an event; bro.


P.S. No offense intended.
ppv117
Posted: Friday, April 11, 2014 4:40:26 AM
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Consider a hot summer in India. By 3pm, the road is about 60 C, walls, terraces and all are anything from 40 - 50 C.

Within an hour or two after sunset, temperatures have fallen by at least 10 degrees celsius and continue to fall through the night to even 25 C.

Where has all the trillion and zillion of kcal gone ? Who absorbed this heat ??? Not air of course, because it itself cools to a nice bearable temp soon after sunset.


Barely literate
Posted: Friday, April 11, 2014 5:34:34 AM

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Your question reminds me another classroom joke. It goes like this...

A teacher asked a question to the pupils in the math class.
"One day, I went on my cycle to the market. On the way I bought half kilo of pumpkin @Rs20 and 1 kg of onion @ Rs30/- and found that there was no air in the back tyre of my cycle. Then I went to a nearby repairing shop to get the air filled and reached home about 6 pm. Now tell me students, how old I am?"

While other students were busy finding answer, one student stood up and said. "Aren't you 54?"

The teacher was stumped at the accuracy of the answer. He congratulated him and asked "How did you get the answer so accurately?"

The student replied "I have a neighbour who is chained up in his room. He, at times, says nonsenses. Everyone says he is half mad. He is 27 yrs. So, I just doubled the figure to arrive at your age!"
ppv117
Posted: Friday, April 11, 2014 9:06:04 AM
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So Salesh....what's my age,then ?

All in good fun. But my poser is not a joke !

Any answers forthcoming ?

I have an answer but I do not have what I may call an authoritative answer printed somewhere.

Felipe Augusto
Posted: Tuesday, April 15, 2014 2:07:27 AM

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Atmosphere?

It's more of a physics question rather than a math one.
Nd:YAG
Posted: Tuesday, April 15, 2014 2:42:35 AM

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The energy absorbed by the ground during the day is radiated away during the night as infrared radiation. Than it is absorbed at higher levels by water vapor(~18 km altitude) and ozone (~40 km altitude), which reradiate that again. This process causes the greenhouse effect and keeps the earth temperature in bearable levels.
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