Age Age Year

Number Theory Level 2

A famous mathematician, Rohit the Great, considered himself lucky. In 1864 , he wrote:

"At some point in my life, the square of my age is equal to the year "

When was Rohit the Great born ?

As an explicit example, if you were 35 years old in the year 1225 , then since 35 * 35 = 1225, thus the square of your age is equal to the year. This does not happen very often.

None of these 1849 1821 1806

3 solutions

Shashvat Shukla
Apr 23, 2014

$42^2=1764$ , $43^2=1849$ , $44^2=1936$ Assuming time machines do not exist, It is unlikely that Rohit the Great was 42 in 1764 as he would have to live at least 142 years for him to be able to write in 1864. Smaller square years give even worse answers. He could not have been 44 in 1936 as then he would have to be born in 1892 and would not be able to write in 1864. Therefore being 43 years old in 1849 is the best answer and so he was born in $1849-43=1806$

Nice solution...

Rohit Nair - 7 years, 1 month ago

Arya Samanta
May 24, 2014

Well I Just kept finding squares from $40$ to $45$ and subtracted the same no.

$\mathtt{To MY delight it was 43.}$ $\boxed {Hence the answer is 1806}$

Long Live Rohit the Great with Arya

$\mathbb{Enjoyed :)}$

Uahbid Dey
May 4, 2014

√1864 = 43.17 Try 44² = 1936 => practically not possible, since future case. try 43² = 1849 => possible 1849 ─ 43 = 1806 => birth year

Age Age Year

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