Tulsidas meets Maharana Pratap

Number Theory Level 3

Assume today is 1st January 2015. I planted a tulsi plant with 0 leaves. Each successive day, the plant gains 2 leaves starting from 2nd January. Let N be the number of leaves on the plant at the end of the year 2020. Find the remainder when N is divided by 7

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Vighnesh Raut by Vighnesh Raut , 23, India

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2 solutions

Vaibhav Prasad
Mar 9, 2015

In the year 2015 there will be 364 364 days when leaves emerge. Thus 2 × 364 = 728 2 \times 364 = \boxed{728}

The years 2016 and 2020 will be leap years so the number of leaves will be 2 × 366 × 2 = 1464 2 \times366 \times 2 = \boxed{1464}

The \years 2017, 2018, 2019 will not be leap and hence the number of leaves will be 2 × 365 × 3 = 2190 2 \times 365 \times 3 = \boxed{2190}

Total = 728 + 1464 + 2190 = 4382 728+1464+2190 = 4382

4382 ≡ 0 ( m o d 7 ) 4382\quad \equiv \quad \boxed{0}\quad \left( mod\quad 7 \right)

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Jahnvi Verma
Mar 9, 2015

In 2015 there will be 364 days after Jan. 1, similarly counting the total no. of days : no. of days for which the plant will grow=364+366+365+365+365+366=2191 no. of leaves in 1 day=2 no. of leaves in 2191 days=2191*2=4382 4382\7=626 with 0 as the remainder

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nice and direct solution.. Upvoted.. and @Vighnesh Raut good to see you thought f this question with the current ongoing track of the series.. but yeah i suggest you keep the name a bit more relevant to the question..!! Cheers and best of luck for your exams..

Harshvardhan Mehta - 6 years, 3 months ago

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