Brainsteem Quickfire Q5 [Win 40% and 10% in SBD]
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The Question
Bertie is celebrating his birthday today with his university friends. One of them notices that Bertie's age is equal to the sum of the digits of the year he was born.
How old is Bertie?
Easy!
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I'm going to take a different approach. The highest possible sum of digits is 28, for someone born in 1999. Now 1999 itself doesn't work out as such a birthday student would only be 18 today, but it provides a limit for the earliest possible birth year, which would be 1989. The digits of 1989 sum up to 27, so that's out.
Now given a 4-digit birth year ending in 9, if we know such a person's age and their birth year's digital sum, we also would realize that for every year earlier that they are born, up to a maximum of 9 years, their age increases by 1 and the sum of their birth year's digits decreases by 1. So if the difference between the age and the digital sum of the birth year in xxx9 is even, we can find a solution in that decade. Applying this to 1999 (digital sum 28, age 18), we see that we go back five years to find a solution in 1994 (digital sum 23, age 23).
We can't find a solution in the decade going back from 2009 (digital sum 11, age 8).
We can find a solution from 2019 (digital sum 12, age -2). Go back 7 years to 2012 (digital sum 5, age 5).
The youngest college student in history that I'm aware of Michael Kearney, who graduated from high school and started attending college at age 6. Thus the concept of a 5-year old attending college is not too far-fetched. Therefore, I say that the university student was most likely born in 1994, but could've been born in 2012.
He was born in 2012 and 5yo :)
He's genius to have uni fds at age of 5 :D
I take this kind of approach :
College years normally starts from 16 upwards. In US, normally it is 18 I think. So, since the question asks that his age by now is equal to the sum of the digits as he was born. We can eliminate the year 2000 and up. Because the highest possible sum of numbers is 11 (year 2009).
And by looking, the year 1990's and up should be the year Bertie was born because the ages on those bracket are from 17 - 27 (year 2000 and 1990) - The possible years a college student's age. All we need to do now is to find a year that has the sum of the digits equal to the difference on today year (2017).
By trial and error (I would recommend this method since there are only 11 possible trials). We can find out that the year 1994 best fits the criteria given by the problem. Take a look at this :
1994 = 1 + 9 + 9 + 4 = 23
2017 - 1994 = 23.
In digital form, the year in which he was born should be written as
n_3 n_2 n_1 n_0
So, what the problem is saying is that
2017 - (1000 n_3 + 100 n_2 + 10 n_1 + n_0) = n_3 + n_2 + n_1 + n_0
or
2017 = 1001 n_3 + 101 n_2 + 11 n_1 + 2 n_0
Now, we can either have n_3 = 1 and n_2 = 9; or n_3 = 2 and n_2 = 0. In the second case we get the equality
2017 = 2002 + 11 n_1 + 2 n_0 <=> 15 = 11 n_1 + 2 n_0.
The only way to satisfy this equation within the natural numbers is with n_1 = 1 and n_2 = 2.
2017 = 1910 + 11 n_2 + 2 n_0 <=> 107 = 11n_1 + 2 n_0
This can be satisfied with n_1 = 9 and n_0 = 4. Since Bertie is in university, this has to be the answer. So, he was born in 1994.
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