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# Puzzles

## Four integers

$$a$$, $$b$$, $$c$$ and $$d$$ are four positive (and non-zero) integers.
$$abcd+abc+bcd+cda+dab+ab+bc+cd+da+ac+bd\\+a+b+c+d=2009$$
What is the value of $$a+b+c+d$$?

## Times roamin'

What is the product of this series?
$$(x-a)(x-b)(x-c)...(x-z)$$
Tags: algebra

## x to the power of x again

Let $$y=x^{x^{x^{x^{...}}}}$$ [$$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ...))) with an infinite number of $$x$$s]. What is $$\frac{dy}{dx}$$?

## x to the power of x

If $$x^{x^{x^{x^{...}}}}$$ [$$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ...))) with an infinite number of $$x$$s] is equal to 2, what is the value of $$x$$?

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