Floor and Ceiling Functions

Floor and Ceiling Functions: Level 2 Challenges


1×2×3×4××100\lfloor1\rfloor\times\lfloor2\rfloor\times\lfloor3\rfloor\times\lfloor4\rfloor\times\cdots \times\lfloor100\rfloor

Find the trailing number of zeros of the product above.

Notation: \lfloor \cdot \rfloor denotes the floor function.

Find the number of trailing zeros in the following expression.

1!2×2!2××30!2.1!^2 \times 2!^2 \times \cdots \times 30!^2.

If xx is an irrational number, what is the value of {x}\left \lceil \left \{ x \right \} \right \rceil?


True or false:

\quad For any real number xx, the value of {x}\{x\} can never be 1.

Notation: {} \{ \cdot \} denotes the fractional part function.

Let 3a 3^a be the highest power of 3 that divides 1000! 1000! . What is a a ?

Note: 1000!=1×2×3×999×10001000! = 1 \times 2 \times 3 \ldots \times 999 \times 1000.


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