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# Another Brain Teaser!

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### It was Madan’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 7 children in the class, how many total handshakes were there?

If you give up here is the answer:

MathsGod1  Mar 25, 2015

#8
+93289
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Yes you can and it is a little easier but it is a starting point to learn LaTex and with LaTex you can present a lot more things than you can with the calculator.

Look at the table Heureka added on this thread.  You could not do that with the calculator!

Almost all Heureka's and my good presentations are done using LaTex.

Melody  Mar 28, 2015
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Well, MG1....I'll take the plunge, here.

Note that the first child shakes 6 other hands.

The second child shakes 5 other hands - he/she has already shaken the hand of the first child.

The third child shakes 4 other hands.....since he/she has already shaken the hand of the first two.

So, continuing likewise, we have.....

6 + 5 + 4 +.....+ 1   =   (6)(7)/2   = 21 handshakes in all

CPhill  Mar 25, 2015
#2
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$$\small{\text{  \begin{array}{|c|c|c|c|c|c|c|c|} \hline \mathrm{child} & #1 & #2 & #3 & #4 & #5 & #6 & #7 \\ \hline #1 & x & {(1,2)} & {(1,3)} & {(1,4)} & {(1,5)} & {(1,6)} & {(1,7)} \\ \hline #2 & & x & {(2,3)} & {(2,4)} & {(2,5)} & {(2,6)} & {(2,7)} \\ \hline #3 & & & x & {(3,4)} & {(3,5)} & {(3,6)} & {(3,7)} \\ \hline #4 & & & & x & {(4,5)} & {(4,6)} & {(4,7)} \\ \hline #5 & & & & & x & {(5,6)} & {(5,7)} \\ \hline #6 & & & & & & x & {(6,7)} \\ \hline #7 & & & & & & & x \\ \hline \end{array}={(21)} \ \mathrm{handshakes} }}$$

heureka  Mar 25, 2015
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Thanks for those great answers Chris and Heureka,

Heureka, I love the LaTex, I never would have thought to present it that way but it looks fabulous. :)

Melody  Mar 26, 2015
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Nice, i had a similar method like CPhill, but i have no idea what LaTeX is.

(I'll need harder brain teasers!)

MathsGod1  Mar 26, 2015
#6
+93289
+5

Hi MG,

Heureka has written his answer in LaTex.

If you hover your mouse over his grid you see a box come up underneath with strange looking stuff in it.  Well that is LaTex.  It is a code that some of us use when we present our mathematics.  It makes it look better.

If you start a new post, you can open up the [LaTex Formula] box, which is in the ribbon at the top.

Then type in

\frac{2}{3}

then press ok

this is what you will see

$$\frac{2}{3}$$

now you have learned how to write a fraction in LaTex.

Melody  Mar 27, 2015
#7
+4664
+5

but instead of using LaTeX to write fractions can't i just use the calculator and do it it seems much easier?

MathsGod1  Mar 27, 2015
#8
+93289
+10

Yes you can and it is a little easier but it is a starting point to learn LaTex and with LaTex you can present a lot more things than you can with the calculator.

Look at the table Heureka added on this thread.  You could not do that with the calculator!

Almost all Heureka's and my good presentations are done using LaTex.

Melody  Mar 28, 2015