Why only E ( m ) E(m) ?

Number Theory Level 3

Let E ( m ) E(m) denote the number of even digits in m m , for example, E ( 2 ) = 1 , E ( 19 ) = 0 , E ( 5672 ) = 2. E(2)=1,E(19)=0,E(5672)=2.

Find E [ E ( 101 ) × E ( 201 ) × E ( 301 ) × ⋯ × E ( 2001 ) ] . E[E(101)\times E(201)\times E(301)\times\dots\times E(2001)].


The answer is 1.

Ayush G Rai by Ayush G Rai , 20, India

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1 solution

Prince Loomba
Jun 21, 2016

E (1×2×1×2×1×2×1×2×1×2×1×2×1×2×1×2×1×2×1×3)=E (1536)=1

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