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Algebra Level 5

There exists a sequence whose terms are a 1 , a 2 , , a 72 a_{1}, a_{2}, \ldots, a_{72} satisfying the following conditions:

(1): a i { 0 , 1 } { a }_{ i }\in \left\{ { 0 },{ 1 } \right\} for all 1 i 72 1 \le i \le 72

(2): a i + 9 + a i + 10 + + a i + 16 > a i + 1 + a i + 2 + + a i + 8 { a }_{ i+9 }+{ a }_{ i+10 }+\cdots+{ a }_{ i+16 }>{ a }_{ i+1 }+{ a }_{ i+2 }+\cdots+{ a }_{ i+8 } for all 0 i 56 0 \le i \le 56 .

Find the value of a 38 a_{38} .


The answer is 1.

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1 solution

Rishabh Jain
Feb 25, 2016

You should change the format of the question to MCQ since answer could be either 0 and 1 and you have got 3 attempts to answer. Hence there is 100% chance of getting the question right!!

I was so happy to see that you posted the solution, but I felt trolled seeing this.

I basically made this question as proof problem.

Department 8 - 5 years, 3 months ago

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Hahahahahahahahahahahhahahahahahhahah,Did sAme .ENter 0 or 1 And see the magic.Its better to be a fool than a mathematician Sometimes.Loved this question

Kaustubh Miglani - 5 years, 3 months ago

I have an idea! make it in binary (y)

Terza Reyhan - 5 years ago

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