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#### Arithmetics. Mental maths , Mathematical logic (other)

Carpenters were sawing some logs. They made 10 cuts and this produced 16 pieces of wood. How many logs did they saw?

#### Examples and counterexamples. Constructive proofs , Mathematical logic (other)

Among 4 people there are no three with the same name, the same middle name and the same surname, but any two people have either the same first name, middle name or surname. Can this be so?

#### Odd and even numbers , Polynomials with integer coefficients and integer values , Rational and irrational numbers

Are there such irrational numbers a and b so that a $>$ 1, b $>$ 1, and [$a^m$] is different from [$b^n$] for any natural numbers m and n?

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