# How to solve this North and South Sitting arrangement puzzle?

10 friends A,B,C,D,E,F,G,H,I,J are sitting in a row. Some of them are facing north while others are facing south. Not more than 2 persons facing the same direction sit together. They all have their birthdays in different months of the same year. Persons born in consecutive months are not sitting adjacent to each other. C sits 4th to right of A, who sits at one of the extreme ends. Only 4 persons face to the south. No one has a birthday in April or in May. C has a birthday in a month which has 30 days. The person having a birthday in February sits to the immediate right of the person having a birthday in October, and both face the same direction. D, who has a birthday in September, sits fourth to the left of B, whose direction is opposite that of A. F has a birthday in August. Neither B nor D is an immediate neighbour of C. E, who has a birthday in March, sits to the immediate right of J, who is 3rd to left of the person who has a birthday in January. I neither faces south nor has a birthday in October.

Now the questions:

1. Who has a birthday in December?

2. Who sits 2nd to right of the person who has a birthday in June?

The question has been taken from a source called Practice Mock. Will full permission of reproduction.

• Is "to the right of X" considered from X's point of view or from an outside observer's? Apr 21, 2022 at 8:22
• X's point of view @msh210
– user79566
Apr 21, 2022 at 10:01
• Are they sitting in a row oriented east-west? Apr 21, 2022 at 13:21
• So we know that A must be at the far left end, and C fourth to the right. I can't figure out other things just yet, but I'll work on it.
– user79541
Apr 21, 2022 at 13:50
• To clarify: here's a helpful table. ~ means NOT. We need to know 3 things: orientation, month, and position A: 1, *, * B: *, *, ~A C: 4, *, * D: *, Feb, * E: *, Mar, * I: *, ~Oct, Nor
– user79541
Apr 21, 2022 at 14:14

This was a fun puzzle. Thanks for posting it.

I think it needs more conditions because I found 2 different answers and strongly suspect that there are many more.

Who has a birthday in December?

I and A

Who sits 2nd to right of the person who has a birthday in June?

D and B

Edit: Here was my thought process:

I started with a diagram representing all possibilities, and then deleted the things that were not possible, step by step. And I had to go back through the steps over and over. Finally, when I was out of clues to apply, I started making guesses and comparing the final results to the rules and to each other. I never finished that final step because I immediately found duplicates. (You may have to zoom in a bit on your browser to really see the details in the pics below.)

Note: Sometime during the process of solving this, I realized that the North-South issue could be solved at the end when I set all of the direction arrows that had not been set, so there is no need to keep 2 separate diagrams (1 for each direction), since one will always be 180° of the other.

At this point, I didn't see anything else that I could cross out, and eventually decided to try different scenarios based on the following two rules that were not yet fully applied/resolved:

1. E, who has a birthday in March, sits to the immediate right of J, who is 3rd to left of the person who has a birthday in January. (since there are just 2 possibilities), and
2. The person having a birthday in February sits to the immediate right of the person having a birthday in October, and both face the same direction. (3 possibilities)

Here are the 6 possibilities I found:

At this point I took the results and removed the rest according to the rules. I did that with one of the other resulting diagrams and they both matched the rules, so I stopped my analysis and posted what I had.

Since I quickly found multiple different layouts that answered the questions differently, I highly suspect that there are many more different layouts that would fit all the rules. A fun puzzle, nevertheless.

• Hey, welcome back JLee! Looks like your first post here since the glory days of 2015 :-) Apr 23, 2022 at 18:32
• Yeah, I missed you guys. I'm back!
– JLee
Apr 23, 2022 at 18:33
• Since the title asked "how to solve" perhaps you could walk through it a bit? Apr 23, 2022 at 18:41
• I also got lost in too many possibilities. Apr 23, 2022 at 21:06