This Pied Piper of Hamelin


Here is just a taste of the results with 720 qne 600 legs showing the ratios of rats to humans nad humans to rats.

pic 1

Lara, John-Anthony, Harry and Richard of Loretto Junior say: If you start with 100 rats and 100 humans and then do the following: Humans 98 and rats 101 Humans 96 and rats 102 And so on -- then you get a lot of combinations!! Yes - you're right, well done. That's a great way to start. So, everytime you have one more rat, you need to lose two humans so that the total number of legs stays at 600. Is it possible to have more than 100 humans then and fewer than 100 rats? We'd love to hear from you if you've investigated this problem further.Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.

Thanks to all who sent in solutions. Here are some from Oakley School and St. George's school. This is what Emily sent us;


If you TAKE 1 rat you have to ADD 2 people
E.G
2 people + 196 rats 98 people + 101 rats
4 people + 195 rats 96 people + 102 rats
6 people + 194 rats
8 people + 193 rats
10 people + 192 rats
etc.
Hope this helps!

Ben, Hannah & Scott sent in these thoughts;

We figured that if you add 1 rat and take 2 people. For example 108 rats and 84 people, 109 rats and 82 people and 110 rats and 80 people.

Otis, Jason & Sophis sent their solutions for 600 legs;

our solutions are:
298 people, 1 rat
298x2 = 596 legs
1 rat = 4 legs
298 people(596 legs) + 1 rat(4 legs)

150x2 = 300 legs
75x4 = 300 legs
150 people(300 legs) + 75 rats(300 legs)