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Rodolfo's birthday

Rodolfo's birthday

Rodolfo Kurchan tells us the following:

Knowing that in 2007 I turned a square number of years, if I add the day and the rest of the month I was born to the sum of the digits of the year I was born, I also get this number, but if I multiply the month and day From my birth I get this number invested and the same happens by multiplying the digits of the year I was born.

Can you tell when it's my birthday?

Solution

He was born on March 21, 1971.

The initial candidate numbers at Rodolfo's ages would be 16, 25, 36, 49, 64, 81, 100? which correspond to the years of birth: 1991, 1982, 1971, 1958, 1943, 1926 ...

The products of its digits give: 81, 144, 63, 360, 108, 108.

The only one that invested gives a square is 63 (gives 36).

Therefore he was born in 1971 and turns 36 years old.

As the product should give 63 (the month for the day) The candidates are (for day and month):

7 and 9
9 and 7
21 and 3

As the sum of the digits of the year of birth is 18, so that the condition that by adding the sum of the day with the subtraction of the month den 36, one must choose 21 and 3.