Arranging the tables
Problem
There are $44$ people coming to a dinner party. There are $15$ square tables that seat 4 people - one at each side - like this:
Or the tables can be joined together to make groups like this:
And so on...
Find a way to seat the $44$ people using all $15$ tables, with no empty places.
Student Solutions
Joshua from Brooklands Primary, Brantham, Suffolk has sent in his first solution - and it's excellent!
First of all I realised that you couldn't seat 44 people around 15 single tables so I started to work out how many people could sit around a certain number of tables pushed together. I made this chart:
| No. of tables pushed together | No. of people |
| 1 | 4 |
| 2 | 6 |
| 3 | 8 |
| 4 | 10 |
| 5 | 12 |
| 6 | 14 |
| 7 | 16 |
| 8 | 18 |
| 9 | 20 |
| 10 | 22 |
| 11 | 24 |
| 12 | 26 |
| 13 | 28 |
| 14 | 30 |
| 15 | 32 |
I then noticed that even if you pushed all the tables together you could only seat 32 people.
I needed to have a mixture of single tables and tables pushed together. I guessed at 4 single tables, which would seat 16 people. That would mean there were still 28 people left, and I only had 11 tables which could sit 24 if pushed together.
Then I saw that 6 single tables would sit 24 people (6x4). I would have 9 tables left which could sit 20 people if tables pushed together. That's my solution!
Jade ( Tattingstone Primary, UK) noticed a pattern in the number of people at the tables too.
I worked it out by timesing 4 by 15 which is 60 places and you only need 44. And every time you join a table you lose two places. So kept joining until I had one table of 8 and 6 tables of 6.
Josh ( Ampthill, Bedfordshire) agrees:
First put nine tables together in a line, which will have 20 people sat there. Then have six tables on their own with four people round each one, That makes another 24 people to give 44 altogether.
During the early part of 2015 we had a number of solutions sent in, in the form of some pictures from Year 6 at Riverdale primary School in Redcar.
Here is a bit of one of them
You can see all the results here .doc or.pdf
Thank you for these latest ones.
Teachers' Resources
Arranging the Tables
There are $44$ people coming to a dinner party. There are $15$ square tables that seat 4 people - one at each side - like this:
Or the tables can be joined together to make groups like this:
And so on...
Find a way to seat the $44$ people using all $15$ tables, with no empty places.