Problem

n machines of factory A and 13 machines of factory B has produced together

n2 +10n -14 articles. Each machine produced the same number of articles.

Which factory has a greater number of machines ?

Answer Submission Is Not Available

Form is valid through June 2017

Solution

Dear visitors and friends of the site!

Thank you for your numerous solutions submitted in June.

Sadly, none of them was perfect.

Here is my solution:

n2 +10n-14 is a multiple of (n+13),

so the same holds for n2 +10n - 14 – (n+13)(n-3) = 25.

Hence, n+3 is a factor of 25, so n not greater than 12.

Thus factory B has more machines.

Have a great summer.

Next problem will appear on the 1st of June.

With best wishes, Serge Hazanov