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Number Theory Level 2

Bhanupratap Singh was born in 19th century. He was crowned as the king after his father when he was x years old and the year was x squared. He reign successfully and died in 1896. What was the year in which he was born?

The answer is 1806.

1 solution

Prajwal Kavad
Apr 8, 2014

Since Bhanupratap was born in 19th century and died in 1896, he must be crowned between 1800 and 1896.

Now, 422 = 1764 (It does not lie between 1800 and 1896) 432 = 1849 (It lies between 1800 and 1896) 442 = 1936 (It does not lie between 1800 and 1896) Thus, Bhanupratap was crowned in the age of 43 years in the year 1849. Hence, the year in which Bhanupratap was born = 1849 – 43 = 1806

Good solution!

At first I couldn't follow the logic because the exponent '2' was displayed as a simple digit 2, e.g. 422 = 1764.

I think the solution should read:

Since Bhanupratap was born in 19th century and died in 1896, he must be crowned between 1800 and 1896.

Now, ${42}^2 = 1764$ (It does not lie between 1800 and 1896) ${43}^2 = 1849$ (It lies between 1800 and 1896) ${44}^2 = 1936$ (It does not lie between 1800 and 1896) Thus, Bhanupratap was crowned in the age of 43 years in the year 1849. Hence, the year in which Bhanupratap was born = 1849 – 43 = 1806

Michael Fischer - 6 years, 9 months ago

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The answer is 1806.

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