Floor Function: Can you solve?

Algebra Level 4

Find the number of ordered pairs ( x , y ) (x,y) satisfying the equation 2 ⌊ sin ⁡ 2 x − cos ⁡ y + 1 ⌋ + 1 = 2 ⌊ cos ⁡ y ⌋ 2\lfloor \sin^2x - \cos y + 1\rfloor + 1= 2 \lfloor \cos y \rfloor .

Notation : ⌊ ⋅ ⌋ \lfloor \cdot \rfloor denotes the floor function .

5 11 3 1 cant be determined 7 0 infinite

Prince Loomba by Prince Loomba , 21, India

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1 solution

Prince Loomba
Apr 14, 2016

Relevant wiki: Floor Function

Left hand side of the equatiom is 2A+1 whereas right hand side 2B, where A and B are integers. Thus LHS=odd and RHS=even. Therefore no solution!

8 Helpful 0 Interesting 0 Brilliant 0 Confused

nice problem bro.

Amrit Anand - 4 years, 12 months ago

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Thanks anshu.

Prince Loomba - 4 years, 12 months ago

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