Erection In The Office

high [The Problem of the Week] The neighbors

This is another old problem of the week that I included in the web Dodka:

Dani's grandfather, which is a nice man who already turned 70 but he still needed to reach 80, and Laura's father, who is in his forties, living in the same street, on the sidewalk of the pairs and adjacent buildings. Laura notes that the product of the age of his father by the number of house you live portal is the product of the age of the grandfather of Daniel for the number of your portal. Estimated the ages of two and the numbers of their homes.


Below as always, is the solution.

[The picture we have chosen today is the facade of Sherlock Holmes Museum on Baker Street. The famous fictional detective always stood out to solve his cases with his keen sense of detail and irresistible logic capability. Arthur Conan Doyle Sherlock Holmes asserts that lived at 221B Baker Street, but that number does not really exist, because at the time that Doyle wrote the stories of street numbering only reached 100. Later in the twentieth century, the street was widened, joining the previously known as Upper Baker Street, and eight numbers, among which included the 221, were assigned to a building called the Abbey House, which since then started to receive an enormous correspondence from around the world aimed at the famous detective. Received so many letters that the Abbey Road Building Society, the construction of the building, had to appoint a "permanent secretary of Sherlock Holmes" to take charge of such correspondence. The image and all information is taken from this web.]

Solution:

This is a matter of trial and error but in which, like Sherlock Holmes did, we must use logic to rule out possibilities and stay with the only valid solution. If we call D at the age of the grandfather of Dani, d the number where you live, L at the age of the father of Laura and l the number where you live, then:
D • d = L × l
If we put aside the ages and numbers of other websites, then:
D / L = l / d
What interests us is that this equality ages are the same proportion or reason that the house numbers. D is a number between 70 and 79, and L is a number between 40 and 49. Then the ratio of the minimum age is 70/49 = 1.42857, and at most 79/40 = 1.975.
Both people living in adjoining houses on the sidewalk of the couple. The numbers of sites may be 2 and 4, 4 and 6, 6 and 8, 8 and 10, etc. But the reasons for each pair of numbers are: 4 / 2 = 2, 6 / 4 = 1.5, 8 / 6 = 1.3333, 10 / 8 = 1.25, etc.. He quickly concludes that the house numbers must be 4 and 6, to be in a proportion consistent with the ages, D and L, for other couples have a right too high (4 / 2 = 2) or too small (8 / 6, 10 / 8, etc.).

Once we have this, we tested pairs of ages that are in the same ratio as 4 to 6, and found that the only numbers that meet this requirement are 48 and 72, 72 / 48 = 1.5, thus Dani's grandfather is 72 and Laura's father 48 and living at number 4 and number 6 respectively.