Math mini-contest problem for Day 6 on D.Buzz for April 2021 😎

in D.Buzz2 months ago

Math problem for Day 6 on D.Buzz 😎

In a D.Buzz gathering where the participants' seats form a convex polygon, @jancharlest arrived late and snuck a seat, causing the average of the interior angles to increase by 4°. How many seats were there before @jancharlest arrived?

Sort:  

hmm, I say there is no solution. What @jfang003 solved is when the sum of interior angles increases by 4 deg. What I understand from the problem is that the average of the interior angles should increase by 4 degree, which means that the sum of interior angles has to increase by 4(n+1) (with n = number of chairs before @jancharlest arrives):

180(n-2)/n + 4(n+1) == 180(n-1)/(n+1)

This equation has no natural/integer solution, only n=3.841 which doesn't work for a number of chairs :)

My answer is 9.

I kind of brute forced it.

180(9-2)/9 = 140
180(10-2)/10 = 144

Loading...