Waste less time on Facebook — follow Brilliant.
×

The seating arrangement problem, version 2

Professor Plum has a dinner party with n² guests. Her guests are seated at n tables, with n guests at each table. After each dish, a new seating arrangement is made so that every guest sits down at a table with guests they have not already shared a table with.

Can every guest share a table with every other guest during the dinner? If not, what requirements do we have on n to allow all the guests to share tables with each other?

(The poster is the original author of this problem.)

Note by Johan Falk
3 years, 6 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Could you, please, mention the resource (the author) of the problem. I liked it very much.

Сергей Кротов - 3 years, 6 months ago

Log in to reply

This is a problem I came up with myself, so thanks! (I'll add a short note on that in the original problem.) I'm sure there are similar problems out there, but so far I haven't seen any.

Johan Falk - 3 years, 6 months ago

Log in to reply

I know that every guest can dine with every other guest if n is a prime number (see version 1 of the problem for comments on this). I've also been told that a similar approach can be used if n is a power of a prime number (eg. n=2^3).

I don't think every guest can meet all other guests if n has more than one prime factor (eg. n=6), but I am not sure.

Johan Falk - 3 years, 6 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...