Answer for Day 10 Math Problem

300 ways 🎯

Solution

(It does not matter which participant gets seated first in the problem, so there are other possible solutions which will give the same answer.)

There are 10 possible ways Manga be seated on any of the 10 seats. That leaves Manga's seat and 2 seats adjacent to Manga (total of 3 seats) excluded from sitting by either Fang or Vision. The new problem will be about "how many ways can 7 people (including Fang and Vision) be seated on a line (no longer a circle) such that Fang and Vision are not beside each other".

• If Fang is seated at either end (2 out of 7 ways), there will be 5 seats Vision can be seated, since there is only one seat beside Fang that Vision cannot occupy. This gives 10 total possible combinations.
• If Fang is not seated at either end (5 out of 7 ways), there will be 4 seats Vision can be seated, since there are two seats beside Fang that Vision cannot occupy. This gives 20 total possible combinations.

Just add all the possible combinations Fang and Vision can be seated, and multiply them with the number of ways Manga can be seated. (10 + 20) * 10 ways = 300 ways

Winner: none 🤯

Since there is no winner for today, 1 HIVE has been distributed proportionally to the previous days' winners who had also been active on D.Buzz on the day of winning. @jfang003 gets 0.834 HIVE and @holovision gets 0.167 HIVE. 💰

Mentions: @eturnerx (@eturnerx-dbuzz) and @ahmadmanga (@ahmadmangazap)
Special mentions: @chrisrice and @jancharlest 🤯