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AuthorWho is the cleverest of 'em all
sorry, I don't get it...
2^2 = 2*2
2^3 = 2*2*2
2^4 = 2*2*2*2
etc.

This is exponentiation.
I see! thanks
2*3^7
multiply first or expo first?
expo first unless you write it out to 2*3*3*3*3*3*3*3 Then it doesn't matter what order you multiply in, but (2*3)^7 is not the same as 2*3^7. There are very few things you can do before exponents.
What is it's shorter name?
other than exponentiation?
for BrutalStrike: exponent multiplication :P
Until Divit is searching for a new one, I suppose each of us can propose a problem (I hope Divit won't mind). So, for 100 gp:

Add and explain the next logic number in the sequence: 1, 7, 40, 85, ... (Hint: the number is one of the following 3: 190, 7480, 15625.)
For the "bunny" question it states
How many bunnies are in this

The answer would be 1

Previously he said bunny, not bunnies, though I assume hat is not the answer looking for
OK! Forget about the previous (too complex) and focus on this one:

Add and explain the next logic number in the sequence: 1, 6, 31, 156,... (Hint. The number is one of the following 3: 780, 781, 782).

I double the stake.
hard =(
Come on, don't give up! Try! :)
781 (5^n - 1)/4.
Correct! It is called geometrical progression. Prize dispatched. :)
or binary number written with one only
I mean base 5, but forget it I get the prize!
It was sum with i from 0 to (n-1) from (5^i) which is (5^n - 1)/(5 - 1) which is exactly your answer. :)

A new one (very simple). Add and explain the next logic number in the sequence: 7, 1, 8, 2, 8,... (Hint. The number is one of the following 3: 1, 3, 9). Stake: 100 gp.
1 : decimal expansion of e
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