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

avatar

Math problem for Day 6 for March 2021 😎

In a D.Buzz gathering, 32 seats have been prepared such that there are 4 rows and 8 columns. How many ways can Turner and Vision be seated such that they are not adjacent to each other horizontally, vertically, and diagonally?

math mathematics minicontest dbuzz contest
0
0
0.000
8 comments
avatar

402 is my answer. Work below.

0
0
0.000
Reply
avatar

32(31) = 992 = total possibilities

Chance that they are adjacent

  1. Four Corners (3 adjacent) : 4(3)=12
  2. On the border but not the corners( 5 adjacent): ((4-2)+(8-2))5 = 80
  3. The rest(8 adjacent): (4-2)(8-2)(8)-96

992-12-80-96 = 804

Since A and B or B and A are the same, 804/2 = 402 ways.

0
0
0.000
Reply
avatar

804
I agree with @jang003's calculation except the division by two at the end. Turner and Vision are different people and therefore exchanging seats for the same chairs is a different way of seating them.

Posted via D.Buzz

0
0
0.000
Reply
avatar

brute force approach :D

combos = 0
for tu_row in range(4):
    for tu_seat in range(8):
        for vi_row in range(4):
            for vi_seat in range(8):
                if abs(tu_row - vi_row) < 2 and abs(tu_seat - vi_seat) < 2:
                    continue
                combos += 1
print(combos)
0
0
0.000
Reply
avatar

Congratulations @savvyplayer! You have completed the following achievement on the Hive blockchain and have been rewarded with new badge(s) :

You got more than 2750 replies.
Your next target is to reach 3000 replies.

You can view your badges on your board and compare yourself to others in the Ranking
If you no longer want to receive notifications, reply to this comment with the word STOP

Check out the last post from @hivebuzz:

Happy Birthday to the Hive Community
A successful meetup and its commemorative badge
0
0
0.000
Reply
avatar

Answer for Day 6 Math Problem

804 ways 🎯

Solution

For simplicity in explaining this solution, we assume that Turner and Vision are seated one after the other (in this case, Turner then Vision).

There are 32 ways Turner can be seated.

  • If Turner is seated at a corner, Vision has 28 seats left. There are 4 corner seats.
  • If Turner is seated on any edge excluding corners, Vision has 26 seats left. There are 16 edge seats excluding corners.
  • If Turner is seated somewhere not on any corner or edge, Vision has 23 seats left. There are 12 non-edge, non-corner seats.

With the information above, we can get the following:

  • There are 112 arrangements where Turner is seated at a corner.
  • There are 416 arrangements where Turner is seated somewhere on an edge except for corners.
  • There are 276 arrangements where Turner is seated somewhere not on a corner or edge.

There are 112 + 416 + 276 = 804 ways Turner and Vision can sit without being adjacent with each other.

Winner: @minus-pi 🏅

1 HIVE has been sent to @minus-pi's Hive account. 💰

  • @jfang003's answer was almost correct had he not divided by two! @minus-pi noticed the minor mistake that Turner and Vision are different people, which means that there are two ways to Turner and Vision can be seated if there are only two seats.

Mentions: @holovision, @eturnerx (@eturnerx-dbuzz), @ahmadmanga (@ahmadmangazap), @paultactico2, @appukuttan66, and @dkmathstats 🤓
Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🤯

0
0
0.000
Reply
avatar

Thanks, @savvyplayer!
Congratulations on the 2750 replies! :)

Posted via D.Buzz

0
0
0.000
Reply
avatar

Thanks! 🙂

However, I am sad to know that I missed a "Weekly Author" award, because I forgot to post at least once a day. 🙁 I am really so focused on comments. 😅

0
0
0.000
Reply