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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,319

Take the challenge.....

The first one to answer this question gets 100 clean jokes in his or her mailbox, free.................

In a get-together, every person present shakes hand with every other person once......

If there are 91 handshakes in all, how many people attended the party?

Don't take more than 5 minutes for answering this.

Character is who you are when no one is looking.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Let me see

If there was only one person, there would be no handshake

If there were two then there would be one handshake (AB)

With three people there would be three handshakes (AB, AC, BC)

With four there would be be (AB, AC, AD, BC, BD, CD) = 6

With five there would be be (AB, AC, AD, AE, BC, BD, BE, CD, CE, DE) = 10

*brnnggggg*

Oh, no, my five minutes is up!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

MathsIsFun may have run out of time, but he did show everyone an important pattern.

With n people, the number of handshakes would be the (n-1)th triangular number.

This means that with 91 people, there would be the 90th triangular number of handshakes, which is

(90*91)/2=4095 handshakes.

Why did the vector cross the road?

It wanted to be normal.

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**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

I wish I got here quicker......

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

You can still have a go, Rora, just time yourself.

I am obviously not quick enough *sob*

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,319

Well, the answer is 14.

Each person would shake hands with thirteen others,

resulting in 14 x 13 = 182

but a handshake involves two people....

divide that by 2, you get 91...

the way to solve this problem is n(n-1) = 91 x 2 = 182

Solve the equation, you get n=14.

My 100 clean jokes remain with me, ha!

Character is who you are when no one is looking.

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**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Nooooooo! Please share them! Spread the joy!

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,319

Please visit my 'Lots of Jokes' page....

at

http://www.geocities.com/ganesh91569

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I feel really stupid now. I didn't read the question properly at all!

Oh well, at least that happened here instead of in an exam...

P.S. Brilliant avatar!

*Last edited by mathsyperson (2005-06-30 03:09:01)*

Why did the vector cross the road?

It wanted to be normal.

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

[ Insert cruel and sadistic, yet sharply witty, comment here to annoy Rora to the full. ]

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Oh yeah, mathsyperson, it was good until you supersized it! LOL

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,319

We know that at -40 degrees, degree centigrade is equal to degree Fahrenheit.

Can you guess at what temperature degree Fahrenheit would be equal to Kelvin?

Character is who you are when no one is looking.

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

1 degree Fahrenheit = 255.927778 Kelvin

1 Kelvin = -457.87 degrees Fahrenheit

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**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Woah......what's Mr. Potato head doing on front of a box of chips?

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Roraborealis wrote:

Woah......what's Mr. Potato head doing on front of a box of chips?

Yeah, bit of a far out marketing concept, hey?

But on with the puzzles.

Kelvin is just Celsius shifted upwards by 273.16, the idea being that absolute zero is 0° K. This would make room temperature about 293°.

Todays forecast: fine, sunny with tops around 295°

So, convert from °K to °C, then from °C to °F. Ohhh, my poor brain hurts ... someone help me ....

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

°C=K-273.15

°F=1.8°C+32

∴ °F=1.8(K-273.15)+32

Ganesh wants to know when these are the same, so solve y=1.8(y-273.15)+32.

Expand the brackets: y=1.8y-491.67+32

Combine the numbers: y=1.8y-459.67

Add 459.67-y to both sides: 0.8y=459.67

Solve: y=575°F/K to the nearest unit. We can't really be more accurate than that because we don't know the exact value of how much bigger K is than °C.

To keep with the theme of temperature, if you have one bucket of water at 30°C and one at 30°F and drop a ball (that sinks!) into both, which will reach the bottom first?

*Last edited by mathsyperson (2005-06-30 20:26:24)*

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,319

mathsyperson is correct.....neat work....

the exact value is 574.5875 and we take degrees centigrade plus 273..15 as Kelvin temperature....

Coming to his question, the bucket of water would at 30 degrees Fahrenheit would have frozen at thirtytwo degree F! so the ball wouldn't sink in the bucket of water at 30 deg f!!!

Character is who you are when no one is looking.

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