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Marián Varaga (Majo)
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Super aplikácia

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Christmas Trees, Science Style

It's always fun to invite scientists to your parties, as long as you remember that scientists sometimes think about trees differently than other people....

From the hidden text in the original xkcd comic (http://xkcd.com/835/):

Not only is that terrible in general, but you just KNOW Billy's going to open the root present first, and then everyone will have to wait whole the heap is rebuilt.

#ScienceSunday #HolidayScience #scisunABS
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The case of 18 and 81. My 8 year old son noticed that 9+9 = 18, and 9x9 = 81 (18 reversed) and was curious of other examples. I wondered if it holds in other bases.

In base 16:
F + F = 1E
F * F = E1

In base 8:
7 + 7 = 16
7 * 7 = 61

Does it hold in base B? That is:
[1] (B-1) + (B-1) = x*B + y
[2] (B-1) * (B-1) = y * B + x
 
For [1], we can move one of the -1's into the second expression
[1] (B) + (B -1 -1) = x*B + y
and see immediately that x is always 1 and y is always B-2.

In case [2], we have
[2] (B -1) * (B-1) = y * B + x
[2] B^2 - 2B + 1= y * B + x
factoring out a B
[2] (B - 2) * B + 1 = y * B + x

Again, we can see that y = B -2 and x = 1.

So in any base B, the highest digit added to itself is the same as the the number multiplied by itself and the digits reversed.

My son would be pleased by this proof, but I haven't taught him enough algebra yet.

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Interesting idea.
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